I'm in the process of researching summer flights from the U.S. into London and out of Paris. I found some relatively well priced tickets, including on British Air, Iberia, and Finnair. When I looked closer at the flights though I found they were all operated by American Airlines. I wasn't particularly thrilled about flying AA to begin with, but I'm also wondering how all of this worked. If I book through British Air, do I check in at the BA counter or the AA counter? If all the inexpensive tickets for many of the airlines lead back to AA, why not just book through them and maybe save a little trouble down the road if there is a flight cancellation. Would there be any advantages to booking that AA operated flight through Finnair or BA?