Subvarieties in non-compact hyperkaehler manifolds

Let M be a hyperkaehler manifold, not necessarily compact, and $S\cong C{P}^1$ the set of complex structures induced by the quaternionic action. Trianalytic subvariety of M is a subvariety which is complex analytic with respect to all $I\in C{P}^1$. We show that for all $I\in S$ outside of a countable set, all compact complex subvarieties $Z\subset (M,I)$ are trianalytic. For M compact, this result was proven in alg-geom/9403006 using Hodge theory.