  To every affine real arrangement of hyperplanes we associate a family of
diagrams of spaces over the face poset of the arrangement. We show that any
cover of the complement of the complexification of the arrangement is homotopy
equivalent to the homotopy colimit of one of the diagrams. More precisely, we
show that any cover of the Salvetti complex is isomorphic to the order complex
of the poset limit of one of the diagrams. We thus obtain explicit simplicial
models for covers of the Salvetti complex.
