(b) Claim in complaint where action commenced by service. In an action which is commenced by service, a claim asserted in the complaint is interposed against the defendant or a co-defendant united in interest with such defendant when: 1. the summons is served upon the defendant; or 2. first publication of the summons against the defendant is made pursuant to an order, and publication is subsequently completed; or 3. an order for a provisional remedy other than attachment is granted, if, within thirty days thereafter, the summons is served upon the defendant or first publication of the summons against the defendant is made pursuant to an order and publication is subsequently completed, or, where the defendant dies within thirty days after the order is granted and before the summons is served upon the defendant or publication is completed, if the summons is served upon the defendant's executor or administrator within sixty days after letters are issued; for this purpose seizure of a chattel in an action to recover a chattel is a provisional remedy; or 4. an order of attachment is granted, if the summons is served in accordance with the provisions of section 6213; or 5. the summons is delivered to the sheriff of that county outside the city of New York or is filed with the clerk of that county within the city of New York in which the defendant resides, is employed or is doing business, or if none of the foregoing is known to the plaintiff after reasonable inquiry, then of the county in which the defendant is known to have last resided, been employed or been engaged in business, or in which the cause of action arose; or if the defendant is a corporation, of a county in which it may be served or in which the cause of action arose; provided that:

(i) the summons is served upon the defendant within sixty days after the period of limitation would have expired but for this provision; or

(ii) first publication of the summons against the defendant is made pursuant to an order within sixty days after the period of limitation would have expired but for this provision and publication is subsequently completed; or

(iii) the summons is served upon the defendant's executor or administrator within sixty days after letters are issued, where the defendant dies within sixty days after the period of limitation would have expired but for this provision and before the summons is served upon the defendant or publication is completed. 6. in an action to be commenced in a court not of record, the summons is delivered for service upon the defendant to any officer authorized to serve it in a county, city or town in which the defendant resides, is employed or is doing business, or if none of the foregoing be known to the plaintiff after reasonable inquiry, then in a county, city or town in which defendant is known to have last resided, been employed or been engaged in business, or, where the defendant is a corporation, in a county, city or town in which it may be served, if the summons is served upon the defendant within sixty days after the period of limitation would have expired but for this provision; or, where the defendant dies within sixty days after the period of limitation would have expired but for this provision and before the summons is served upon the defendant, if the summons is served upon his executor or administrator within sixty days after letters are issued.

(c) Claim in complaint where action commenced by filing. In an action which is commenced by filing, a claim asserted in the complaint is interposed against the defendant or a co-defendant united in interest with such defendant when the action is commenced.

(d) Defense or counterclaim. A defense or counterclaim is interposed when a pleading containing it is served. A defense or counterclaim is not barred if it was not barred at the time the claims asserted in the complaint were interposed, except that if the defense or counterclaim arose from the transactions, occurrences, or series of transactions or occurrences, upon which a claim asserted in the complaint depends, it is not barred to the extent of the demand in the complaint notwithstanding that it was barred at the time the claims asserted in the complaint were interposed.

(e) Effect upon defense or counterclaim of termination of action because of death or by dismissal or voluntary discontinuance. Where a defendant has served an answer containing a defense or counterclaim and the action is terminated because of the plaintiff's death or by dismissal or voluntary discontinuance, the time which elapsed between the commencement and termination of the action is not a part of the time within which an action must be commenced to recover upon the claim in the defense or counterclaim or the time within which the defense or counterclaim may be interposed in another action brought by the plaintiff or his successor in interest.

(f) Claim in amended pleading. A claim asserted in an amended pleading is deemed to have been interposed at the time the claims in the original pleading were interposed, unless the original pleading does not give notice of the transactions, occurrences, or series of transactions or occurrences, to be proved pursuant to the amended pleading.

(g) 1. Time computed from actual or imputed discovery of facts. Except as provided in article two of the uniform commercial code or in section two hundred fourteen-a of this chapter, where the time within which an action must be commenced is computed from the time when facts were discovered or from the time when facts could with reasonable diligence have been discovered, or from either of such times, the action must be commenced within two years after such actual or imputed discovery or within the period otherwise provided, computed from the time the cause of action accrued, whichever is longer. 2. Notwithstanding paragraph one of this subdivision, in an action or claim for medical, dental or podiatric malpractice, where the action or claim is based upon the alleged negligent failure to diagnose cancer or a malignant tumor, whether by act or omission, for the purposes of sections fifty-e and fifty-i of the general municipal law, section ten of the court of claims act, and the provisions of any other law pertaining to the commencement of an action or special proceeding, or to the serving of a notice of claim as a condition precedent to commencement of an action or special proceeding within a specified time period, the time in which to commence an action or special proceeding or to serve a notice of claim shall not begin to run until the later of either (i) when the person knows or reasonably should have known of such alleged negligent act or omission and knows or reasonably should have known that such alleged negligent act or omission has caused injury, provided, that such action shall be commenced no later than seven years from such alleged negligent act or omission, or (ii) the date of the last treatment where there is continuous treatment for such injury, illness or condition.