Breeze Airways, the new airline started by David Neeleman, founder of JetBlue, will start flying on May 27. The first flights will connect Charleston, S.C.; Tampa; and Hartford, Conn. Other destinations will be added each week through July 22, stretching from Providence, R.I., to San Antonio. Breeze will start with 13 Embraer jets, some of which it is getting from another Neeleman airline, Brazil’s Azul. Breeze has ordered 60 slightly larger Airbus A220 jets that it expects to begin receiving in October at a rate of one per month, which should let it operate longer flights. Neeleman has said there is an untapped market for nonstop flights between smaller cities. The airline is not offering daily service on any routes, with four times a week the highest frequency. According to the carrier, 95% of its routes have no nonstop competition.