Was Southwest the biggest airline in May? They boarded the most domestic passengers of any US carrier, becoming the first low-fare airline to top the monthly list, according to US Transportation Department statistics released last Tuesday. Southwest edged out Delta Air Lines and American Airlines to claim the top spot. Southwest boarded 6.5 million passengers on its flights, compared with 6.3 million for Delta and 6.2 million for American. Last May, Southwest ranked third.