  In this paper, we study the behavior of Ricci-flat K\"{a}hler metrics on
Calabi-Yau manifolds under algebraic geometric surgeries: extremal transitions
or flops. We prove a version of Candelas and de la Ossa's conjecture:
Ricci-flat Calabi-Yau manifolds related by extremal transitions and flops can
be connected by a path consisting of continuous families of Ricci-flat
Calabi-Yau manifolds and a compact metric space in the Gromov-Hausdorff
topology. In an essential step of the proof of our main result, the convergence
of Ricci-flat K\"{a}hler metrics on Calabi-Yau manifolds along a smoothing is
established, which can be of independent interests.
