  This paper is devoted to the comparison of different localized categories of
differential complexes. The first result is that the canonical functor from the
category of complexes of differential operators of order one (defined by
Herrera and Lieberman) to the category of differential complexes (of any order,
defined by M. Saito), both localized with respect to a suitable notion of
quasi-isomorphism, is an equivalence of categories. Then we prove a similar
result for a filtered version of the previous categories (defined respectively
by Du Bois and M.Saito), localized with respect to graded-quasi-isomorphisms,
thus answering a question posed by M. Saito.
