An American Airlines aircraft. (Tony Gutierrez/AP)

If you think the merger between American Airlines and US Airways is all over but the shouting, think again.

There’s been plenty of excitement so far, from a heated congressional hearing to a controversial settlement agreement with the Justice Department in 2013, which cleared the world’s largest airline for takeoff.

But the best may be yet to come. The airlines expected to merge their loyalty programs by March 28. They’re also busy aligning company policies. And later this year, the carriers will combine their reservations systems, arguably the most difficult part of any merger and perhaps the most noticeable from a customer perspective.

Along the way, there’s been plenty of drama on the ground. Consider what happened to Viviane Tran, an information systems consultant from Washington, who had scraped together 240,000 frequent-flier miles to fly to Tokyo for her honeymoon in April. When US Airways rescheduled her flight, a representative also offered to update the name on her ticket — a routine operation, Tran was assured. It was not.

“I waited for at least 15 minutes; when she finally came back she told me that we’ve lost our seats and she’s unable to re-book us on the same flights because she does not have access to American Airlines’ inventory,” she says. “My husband and I are now without flights to Japan.”

Tran posted a request for help on my forum, and I contacted American. The airline eventually re-booked her on a new flight to Japan with a more convenient schedule.

Their case illustrates how far the merger has come — and how far it has yet to go. The two airlines continue to operate separately, with their own crews, their own rules and their own Web sites. In fact, this corporate combination won’t be fully complete until 2016. And in the meantime, there’s plenty of opportunity for more problems like the one Tran encountered.

The latest merger-related issue is the combination of the two airlines’ loyalty programs, AAdvantage and Dividend Miles. Under the plan, US Airways program members will see their mileage balances transferred into an AAdvantage account on a 1-to-1 ratio. If you’re an elite-level frequent flier, American will determine your status level using a formula that considers your combined elite-qualifying activity for 2014 and your combined 2015 year-to-date elite-qualifying activity. That integration may take a few days to complete, the airline says.

There may be a bump or two along the way. For example, if you want to make a Dividend Miles award booking or a mileage upgrade, US Airways warned its customers to act soon. American expected its systems to be disabled for a few days while the loyalty programs are combined. And for the next few months, it will also handle upgrades differently until some of the information systems can be combined.

For the most part, frequent fliers are taking a wait-and-see approach. They say employees are upbeat about the merger so far, and they find that reassuring.

“The flight attendants, ticket agents and others I interact with seem to be excited for the change,” says Jeffrey Cesari, a Philadelphia-based event planner who is a frequent US Airways customer. “I was just speaking with one of the flight attendants who got back from training. They seem to be excited about the new changes and technology being embraced to provide outstanding customer service.”

Between now and the fourth quarter of this year, most of the merger-related activities will take place behind the scenes. They include harmonizing policies that can affect every part of your trip, such as luggage rules and refund policies. For instance, at present, US Airways will refund your ticket within 24 hours of making your reservation, as long as you’re more than a week away from your departure. American Airlines won’t. Instead, it lets you “hold” a ticket for 24 hours at no charge. Which of these policies will the merged airline have? No one knows yet.

The real test will come this winter, when American and US Airways combine their systems for reserving tickets. That may seem insignificant, but tell that to the hundreds of thousands of United Airlines customers who contended with an IT nightmare in March 2012, referred to by United as simply the “cutover.” It was the final and most difficult piece of the puzzle in the merger with Continental Airlines, and it involved combining two complex passenger reservations systems, as well as several other changes.

On the morning of March 3, 2012, United customers awoke to a new Web site, and the old Continental site now pointed to Airport agents powering up their workstations were greeted by the login screen to a system that half of them hadn’t used in a real-world setting. The system began to freeze up under the weight of the surge of new queries. Calls started to pour in, too many to answer.

Martin Hand, then United’s senior vice president for customer experience, was deluged with angry customers. “My e-mail volume was up by about 10,000 percent,” he told me a month later. “For the first three weeks, I would be up until midnight every day and start again at 5 a.m., answering customers.”

American’s own cutover this year will be the last major obstacle on the runway to a merger, at least from a flier’s viewpoint. It could be an opportunity to win customers with a smooth transition — which happened when Delta Air Lines and Northwest Airlines synced up during their merger — or a chance to drive customers away.

“This one fortunately seems to be more like Delta-Northwest so far — but with the very big caveat that they haven’t yet gone through those difficult systems integrations,” says Seth Kaplan, the editor of Airline Weekly, a trade publication.

In the meantime, as we head into the busy summer travel season, one thing seems clear. Even though American Airlines acts as though it’s a single airline, in some respects, it isn’t. And until it is, there may be a little turbulence ahead.