(a) All actions at law or in equity, or causes in the court of general sessions of any old county where new counties have been formed from the territory of the same, if the parties interested in the suits live in the new counties so formed, and the subject matter of the suits originated within the limits of the new county, upon application of the parties litigant, or either of them, may be removed to the new county.
(b) When the plaintiff and defendant in any litigation both reside in a new county established by law, the litigation, if pending in one (1) of the old counties from which the new county is taken, may be transferred to the court established for the new county, either common law, chancery, or criminal, according to the nature of the case.