The squabble is between carriers and the travel websites that list their ticket prices.
American Airlines has pulled its flights and fares from Orbitz.com, and is no longer listed on Expedia.com, either. Delta Air Lines yanked listings from CheapoAir.com, OneTravel.com and BookIt.com, with, apparently, more sites to come.
The sticking point, CBS News Travel Editor Peter Greenberg explained on "The Early Show on Saturday Morning," is the fees airlines pay those sites - known as online travel agencies - to list their flights and sell their seats.
It's all having an industry-wide ripple effect on the way people buy tickets, Greenberg points out.
But he shared tips to help you navigate your away around their battle and still land the best fares:
In the past, when airlines were flying with a lot of seats empty, they needed as many distribution channels as possible to sell as many tickets as possible. But times have changed. Airlines have reduced capacity over the past 18 months, and planes are flying nearly full - with 87 percent of seats sold. The carriers want to keep more of the ticket revenue and pull back on distribution and its associated fees and sell more of their own tickets on their own websites.
IF YOU WANT TO ONLY SEARCH ONLINE, comparison shop by searching various websites, such as Kayak.com, Fly.com, FareCompare.com, and Momondo.com.
YOUR BEST OPTION is to get on the phone and speak directly with an airline representative or travel agent to compare non-stop and one-stop fares (instead of Dallas nonstop to New York, for instance, Dallas to New York via Raleigh-Durham N.C. could save you $800! Yes, there is a fee to access the airline person, but if you can save $600, a $30 fee is worth it! There's no fee to talk to travel agents. I recommend this route most, because NOT all inventory is on the web.
TAKE ADVANTAGE OF SALES OFFERED THROUGH SOCIAL MEDIA SITES. These tend to disappear more quickly, but they're there. They generate last-minute, incremental revenue for airlines. Most carriers are on Twitter and Facebook now, and will e-mail you offers.
Airlines and travel websites are likely to mend fences at some point, but for now, you have to try a little harder when you comparison shop for fares.