© Taylor Glascock for The New York Times Southwest Airlines canceled most of its flights on Tuesday and Wednesday, leaving many travelers stranded around the country, including at Chicago’s Midway airport. Southwest Airlines canceled thousands of flights on Tuesday and Wednesday, as the company struggled to recover from a deadly winter storm that has left holiday travelers stranded around the country. © Taylor Glascock for The New York Times Customers at Midway contended with delays and cancellations at a Southwest Airlines counter on Tuesday. Making matters worse for customers: Southwest has a policy of not exchanging tickets with other airlines, so the airline could not rebook passengers on other flights, Mr. Harteveldt said. The number of canceled flights began to rise last Thursday, when airlines called off more than 2,600 of them.