Blowing up symplectic orbifolds

In the first part of this paper we study different blow-up constructions on symplectic orbifolds. Unlike the manifold case, we can define different blow-ups by using different circle actions. In the second part, we use some of these constructions to describe the behavior of reduced spaces of a Hamiltonian circle action on a symplectic orbifold, when passing a critical level of its Hamiltonian function. Using these descriptions, we generalize, in the manifold case, the wall-crossing theorem of Guillemin and Sternberg to the case of a Hamiltonian torus action not necessarily quasi-free and also the Duistermaat-Heckman theorem to intervals of values of the Hamiltonian function containing critical values.