  We parametrize the gauge-fixing freedom in choosing the Lagrangian of a
topological gauge theory. We compute the gauge-fixing dependence of correlators
of equivariant operators when the compactified moduli space has a non-empty
boundary and verify that only a subset of these has a gauge independent
meaning. We analyze in detail a simple example of such anomalous topological
theories, 4D topological Yang-Mills on the four-sphere and instanton number
k=1.
