To hear and decide appeals from any decisions of the Building Inspector; to hear and decide applications for special permits as authorized by the Reading Zoning By-Laws; to hear and decide petitions for variances as authorized by the Reading Zoning By-Laws; to hear and decide applications seeking authorization and a Comprehensive Permit to build low and moderate-income housing contemplated by GL c. 40B, Sec. 21; to hear and decide upon all matters otherwise legally coming under the jurisdiction of the Board of Appeals.