On and after the date when a plan has been approved for the betterment of a neighborhood area by the legislative body, no permit shall be issued for building construction, sidewalks, drainage systems or other major improvements done on properties indicated for public improvements which are not in accordance with the plans officially adopted and made effective by the legislative body: Provided, however, That the legislative body shall provide by ordinance that the zoning board of appeals, if the municipality has such a board, or if not, then a board of appeals created for such purpose, shall have the power on appeal filed with it by the owner of real property in the area to approve a minor deviation from the plan for the area in any case in which such board finds upon the evidence presented to it that the application of the plan results in unnecessary hardship or practical difficulties and a minor deviation from the betterment plan is required by consideration of justice and equity. Before taking any such action, the board shall hold a public hearing thereon, at least 10 days’ notice of time and place of which shall be given by public notice in a newspaper published or circulated generally in the municipality and by notice to all property owners within the neighborhood area, such notice to be by mail addressed to the respective owners at the address given in the last assessment roll.