U.S. Anesthesia Partners, which is backed by Welsh, Carson, Anderson & Stowe, said Monday that Greater Houston Anesthesiology P.A. will serve as U.S. Anesthesia’s cornerstone affiliated practice. As part of the deal, U.S. Anesthesia will buy the Greater Houston Anesthesiology assets that provide practice management and business support services. Financial terms were not announced. Greater Houston provides anesthesiology services for major medical facilities in Houston and Austin.