A Leviship is a type of airship which utilizes a Levistone. Examples of leviships include the Crusade and Zaibach's Floating Fortresses. Leviships are different than the airships that appear in Escaflowne, though the Black Dragon Clan floating fortresses may use similar technology.
A leviship uses a levistone, a rock unique to Gaea that floats in midair. Due to it floating mid-air in its "normal state", the rock is heated (usually with power from Energists) to lower it to the ground.
An unknown large Leviship crashes in Episode 26 of the anime.