Section 70A. Whenever upon application for abatement or otherwise any tax, assessment, rate or charge assessed by a board or officer of a town, or any interest thereon or costs relative thereto, is finally abated in whole or in part by any court or officer, or by any board, which latter term as used in this sentence shall include the county commissioners and the appellate tax board, the officer or the secretary, clerk or similar official of the board assessing such tax, assessment, rate or charge shall forthwith give notice of such abatement to the collector and to the auditor, accountant or similar official. If the assessment was made by a board or officer other than the assessors and the tax, assessment, rate, charge, costs or interest is part of an annual tax, such notice shall also be given to the assessors. Upon receipt of such notice, the collector shall make due entry of the abatement in his books, except where the tax, assessment, rate or charge is an item in a tax title account set up under section fifty of chapter sixty, in which case he shall forthwith transmit such notice to the treasurer, who shall forthwith enter the abatement on the tax title account, and the treasurer shall thereby be relieved of further responsibility with respect to the amount abated. Whenever any tax, assessment, rate, charge, costs or interest constituting an item in a tax title account is abated in whole or in part, the account, if any, set up on the books of the town showing the amount of tax title revenue available when collected shall be reduced accordingly. Whenever any tax, which word as used in this sentence shall be construed to mean the tax assessed under this chapter and not to include any assessment, rate, charge, costs or interest added thereto, is abated in whole or in part, whether or not such tax has been collected and whether or not such tax is secured by a tax title held by the town, the amount of the abatement shall be charged against the overlay of the year of such tax.