In this article we are interested in morphisms without slope for mixed Hodge modules. We first show the commutativity of iterated nearby cycles and vanishing cycles applied to a mixed Hodge module in the case of a morphism without slope. Then we define the notion strictly without slope for a mixed Hodge module and we show the preservation of this condition under the direct image by a proper morphism. As an application we prove the compatibility of the Hodge filtration and Kashiwara-Malgrange filtrations for some pure Hodge modules with support an hypersurface with quasi-ordinary singularities.
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