Degeneration of weight spectral sequences

A notion of morphism of semi-stable type is a higher dimensional analogue of semi-stable degeneration over the unit disc. For a proper surjective morphism of semistable type, the author constructed a cohomological mixed Hodge complex which gives a candidate of the limit of Hodge structures. In this article we define finite increasing filtrations on the cohomological mixed Hodge complex above and prove the E-2-degeneracy of the spectral sequences obtained from these filtrations.