Azel and Edge ride a floater.
Floaters are hovercraft that are armed with maintenance lasers, similar to the homing lasers of a dragon. The floaters were created by the Ancients to travel through many floors and passageways of Uru Underground Ruins. When Azel and Edge are separated from their dragons in Panzer Dragoon Saga, the pair use a floater to travel back to the surface.
In Panzer Dragoon Saga's "Data on Defeated Enemies" there is a floater entry listed under "Dragon Models". The floater isn't a dragon but takes on the role of Edge's dragon while it is absent.