In this article we consider a spectral sequence (E(r), d(r)) associated to a filtered Morse-Conley chain complex (C, Delta), where Delta is a connection matrix. The underlying motivation is to understand connection matrices under continuation. We show how the spectral sequence is completely determined by a family of connection matrices. This family is obtained by a sweeping algorithm for Delta over fields IF as well as over Z. This algorithm constructs a sequence of similar matrices Delta(0) = Delta, Delta(1), ... , where each matrix is related to the others via a change-of-basis matrix. Each matrix Delta(r) over F (resp., over Z) determines the vector space (resp., Z-module) E(r) and the differential dr. We also prove the integrality of the final matrix Delta(R) produced by the sweeping algorithm over Z which is quite surprising, mainly because the intermediate matrices in the process may not have this property. Several other properties of the change-of-basis matrices as well as the intermediate matrices Delta(r) are obtained. (C) 2010 Elsevier By. All rights reserved.1571321112130