  In this paper, we describe the spaces of stability conditions for the
triangulated categories associated to three dimensional Calabi-Yau fibrations.
We deal with two cases, the flat elliptic fibrations and smooth K3 (Abelian)
fibrations. In the first case, we will see there exist chamber structures
similar to those of the movable cone used in birational geometry. In the second
case, we will compare the space with the space of stability conditions for the
closed fiber of the fibration.
