  Let k be a commutative ring with unit. We endow the categories of filtered
complexes and of bicomplexes of k-modules, with cofibrantly generated model
structures, where the class of weak equivalences is given by those morphisms
inducing a quasi-isomorphism at a certain fixed stage of the associated
spectral sequence. For filtered complexes, we relate the different model
structures obtained, when we vary the stage of the spectral sequence, using the
functors shift and d\'ecalage.
