Great question, between races the planes are usually transported by a 747! The planes are designed so the wing is one piece and can easily be taken off the plane, the tail also comes off. The wing gets its own box, designed like a suitcase and the tail fits in its own suitcase too. The fuselage is then wrapped for protection and loaded on a air freight pallet, two planes are able to fit on one pallet. Two planes on one pallet help control costs, because if every plane had its own pallet the cost to ship would skyrocket. If the races are in the same country, like the US races between Dallas and Vegas, the planes are simply flown to the next location.
Kirby has a new plane for the 2014 Air Race season, the EDGE V3! It was designed especially for racing by Zivko Aeronautics in Guthrie, Oklahoma.