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In 1960, Smale defined a filtration of a closed smooth manifold by the unstable manifolds of fixed points and closed orbits of a Morse-Smale vector field defined on it, and derived generalized Morse inequalities. This suggests that, similarly to the Morse complex of Morse-Smale functions, even in the presence of closed orbits, Morse-Smale vector fields admit canonical chain complexes, invariant under topological equivalence, from which one can algebraically derive Morse inequalities. We show how to construct such a chain complex by considering the exact couple in Čech homology of the unstable manifolds filtration, and then turning this exact couple into a chain complex such that the infinity page of the spectral sequence associated with the exact couple gives the homology of the constructed chain complex. Time permitting, we discuss the functoriality of the construction and compute some simple examples. This is joint work with Claudia Landi.