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Star Alliance was formed by a couple of airlines in 1997. It was formed for frequent flyers, which they could collect mileage when flying. Enough miles can be redempted for free upgrades and even free tickets. Literally, an Airline Alliance is a team that compormises of different airlines, forming together to offer mileage programmes to frequent flyers. Moreover, airlines in alliances exchange flights each other (codeshare).
What is codeshare flights:
FOR EXAMPLE ONLY:
If United Airlines(a Star Alliance member) wants to fly a route from Washington to Vienna, and US Airways(another Star Alliance member) operates that route, United could offer to codeshare with US Airways. United needs to sponsor half the operating cost of the flights, but in return United gets a four-digit flight number on this flight and could offer booking for passengers.
These practices are commonly seen and I'd belive you had experienced this for at least one time, and to distinguish this your e-ticket might say 'OPERATED BY B AIRLINES' although you have booked through A Airlines.