American Airlines is bracing for short-term passenger anxiety about flying on the Boeing 737 Max. “There may be some period of time’’ in which customers have misgivings, American Airlines Group CE Doug Parker said Wednesday. “But we’ll work through that.’’ Airlines will soon face the delicate task of coaxing passengers back onto Boeing’s best-selling jet, once the aircraft is cleared to return to the skies. “What we need to do is have the airplane be deemed airworthy, be back in service, have American Airlines pilots flying,’’ Parker said. “I know that if that’s the case, the airplane’s 100% safe, as will most of our customers. And over time, others will see that and come to the same conclusion.’’ American has 24 of the grounded jets with more on the way. <br/>