Construction is underway on a 199-foot wireless communications tower at George J. Mitchell Field that should improve cellular service on Harpswell Neck and may boost signals on the islands too. Blue Sky Towers III LLC, of Massachusetts, is building the tower. Work started June 7 and the company expects to finish the tower by Oct. 1, according to Elizabeth Thompson, the company’s general counsel.AT&T is the only carrier with a deal to have equipment on the tower so far, so the project will primarily benefit AT&T customers in the beginning. Blue Sky expects AT&T’s equipment to be operational by Oct. 1.