  We prove that for all ergodic extensions S_1 of a transformation by a locally
compact second countable group G, and for all G-extensions S_2 of an aperiodic
transformation, there is a relative speedup of S_1 that is relatively
isomorphic to S_2. We apply this result to give necessary and sufficient
conditions for two ergodic n-point or countable extensions to be related in
this way.
