There are no commercial flights to Chivay. And that's fine cause the road from AQP is interesting and beautiful. I went by tour, departed from Arequipa at 7am aprox, arriving at Chivay at 3pm aprox.

The usual tours program the canyon visit the next day, very early in the morning as joseeantonior said, with the purpose of catching the condors flight. They said they are seen early in the morning and whenever there's no noise nor many people. Well I went on a long weekend and though we arrived early at the canyon, there were LOT of people, and consequently too much noise. Never mind, I saw several condors, big ones, small ones, adults, youngs... took lot of pictures. It was a beautiful spectacle.

The usual tour get you back to Arequipa that second day, so it is a short tour. Too bad, cause there are several places to see along the canyon. Landscapes, trekking, towns, archeaological sites, etc. I spend a third day on my own and enjoyed a lot. If you are planning to go on your own, renting a car, etc., staying 2 nights is recomendable.

I went in 2010, communications were very limited, just one cybercafe and too slow. It may be improved nowadays, but it's wise to doublé check hotels with wifi if you are interested in keeping connected.