The ticketing carrier is the one that issued the ticket and will "pay" on that ticket when redeemed. It is the first three numbers of the ticket, i.e., 001 is AA, 006 is DL, 027 is AS, etc. It will typically be the same as the marketing carrier, but not always, and typically the airline of the most significant segments of your trip, if not issued by the airline directly (i.e., a travel agent).