  Using our uniqueness in law transfer result for SPDEs, described in a recent
note, we prove the equivalence of laws of SPDEs differing by a drift, under
vastly applicable conditions. This gives us the equivalence in the compact
support property among a large class of SPDEs. As an important application, we
prove the equivalence in law of the Allen-Cahn and the associated heat SPDEs;
and we give a criterion for the compact support property to hold for the
Allen-Cahn SPDE with diffusion function $a(t,x,u)=Cu^\gamma$, with $C\ne0$ and
$ 1/2\le\gamma<1$.
