(b) If a transaction is taxed by both a county and a city, the rate of tax on such transaction imposed by the county or city, not having prior right thereto pursuant to section twelve hundred twenty-four, shall be deemed to be reduced (or the entire tax eliminated, if necessary) to the extent necessary to comply with the foregoing requirement. A tax imposed by a county upon any transaction, to the extent that it would require a reduction in any tax rate imposed thereon by a city, shall not become effective in respect to any transaction taxed by such city (or in respect of other similar transactions outside of the city which, if occurring in such city, would be subject to such city tax) before the commencement of the city's next succeeding fiscal year and then only if the county shall have given notice to such city of its imposition of a tax on such transaction at least six months prior to the commencement of such fiscal year, provided however that the local legislative body of such city may waive the requirement of such notice and the postponement of the effective date of such tax. A city tax upon any transaction, to the extent that it would require a reduction in any tax rate imposed by a county thereon, shall not become effective in respect of any transaction taxed by such county before the commencement of the county's next succeeding fiscal year and then only if the city shall have given notice to such county of its imposition of a tax on such transaction at least six months prior to the commencement of such fiscal year, provided, however, that the local legislative body of such county may waive the requirement of such notice and postponement of the effective date of such tax. However, whether or not the six months' notice requirement provided in this section has been waived, a tax imposed pursuant to the authority of section twelve hundred ten or twelve hundred eleven shall still be subject to the requirements provided for in the first three sentences of subdivision (d) of such sections and in subdivision (e) of such sections.