Based on our work on generic motives, we give a link between the theory of motivic complexes by Voevodsky and the theory of cycle modules by Rost: cycle modules form the heart of the homotopy t-structure on the non effective version DM(k) of motivic complexes. Note this constitutes an evolved version of the Gersten resolution for homotopy invariant sheaves with transfers. As an illustration, we show that the coniveau spectral sequence of a smooth scheme with coefficients in an object of DM(k) coincides with the hypercohomology spectral sequence for the homotopy t-structure. With the concept of mixed Weil theory recently introduced by D.C.Cisinski and the author, this gives a reformulation (and a new proof) of a theorem of Bloch and Ogus.