  We say that an exact equivalence between the derived categories of two
algebraic varieties is tilting-type if it is constructed by using tilting
bundles. The aim of this article is to understand the behavior of tilting-type
equivalences for crepant resolutions under deformations. As an application of
the method that we establish in this article, we study the derived equivalence
for stratified Mukai flops and stratified Atiyah flops in terms of tilting
bundles.
