  Wall-crossing formulas for various flavors of elliptic genus can be obtained
using master spaces. We give a topological criterion which implies that such
wall-crossing formulas are trivial. Applications are given for: GIT quotients,
following Thaddeus; moduli of sheaves, following Mochizuki; Donaldson-Thomas
and Vafa-Witten theory, following Joyce and Tanaka-Thomas respectively.
