(b) No exemption shall be granted for alterations, installations or improvements unless such alterations, installations or improvements were commenced subsequent to the effective date of the local law or resolution adopted pursuant to subdivision one of this section. Notwithstanding the foregoing provision, if such alterations, installations or improvements were commenced prior to the effective date of the local law or resolution adopted pursuant to subdivision one of this section, such alterations, installations or improvements may receive an exemption pursuant to the exemption schedule of this section for the remainder of the authorized period of exemption as if such alterations, installations or improvements had been commenced on or after such effective date; provided, however, the property shall not be eligible for refunds of property taxes or special ad valorem levies paid prior to the effective date of the local law or resolution. 3. Such exemption shall be granted only upon application by the owner or all the owners of such building on a form prescribed by the state board. The application shall be filed with the assessor of the county, city, town or village having the power to assess property for taxation on or before the appropriate taxable status date of such county, city, town or village. 3-a. Notwithstanding the provisions of this section or any other provision of law, in a city having a population of one million or more, applications for the exemption authorized pursuant to this section shall be considered timely filed if they are filed on or before the fifteenth day of March of the appropriate year. 4. If satisfied that the applicant is entitled to an exemption pursuant to this section, the assessor shall approve the application and such building shall thereafter be exempt from taxation and special ad valorem levies as herein provided commencing with the assessment roll prepared on the basis of the taxable status date referred to in subdivision three of this section. The assessed value of any exemption granted pursuant to this section shall be entered by the assessor on the assessment roll with the taxable property, with the amount of the exemption shown in a separate column. 5. A county, city, town or village may, by local law, or a school district may, by resolution:

(i) reduce the per centum of exemption otherwise allowed pursuant to this section and

(ii) limit eligibility for the exemption to those forms of alterations, installations, or improvements as are prescribed in such local law or resolution.