Let X be the blow-up of a smooth projective variety Y along a codimension two smooth closed subvariety.
In this talk, we will construct a sequence of flip-like diagrams connecting the moduli space
of sheaves on Y and that of X. This is a higher dimensional generalization of the Nakajima and Yoshioka's result,
which treats the case when dimY=2. The key technical tool to describe the diagram is Bridgeland's perverse coherent sheaves. As an application of the general result, we will discuss about the birational geometry of Hilbert scheme of two points.