Dynamical Spectral Sequences Over $Z_2$

In this paper, we consider a sweeping method for a chain complex $C$ and its differential given by a connection matrix $\Delta$ over $\mathbb{Z}_2$ which determines an associated spectral sequence$(E^r,d^r)$. More specifically, a system spanning $E^r$ in terms of the original basis of $C$ is obtained as well as the identification of all differentials $d^r$.