  In this paper we build an Orlik-Solomon model for the canonical gradation of
the cohomology algebra with integer coefficients of the complement of a toric
arrangement. We give some results on the uniqueness of the representation of
arithmetic matroids, in order to discuss how the Orlik-Solomon model depends on
the poset of layers. The analysis of discriminantal toric arrangements permits
us to isolate certain conditions under which two toric arrangements have
diffeomorphic complements. We also give combinatorial conditions determining
whether the cohomology algebra is generated in degree one.
