We define the notion of spectral network on manifolds of dimension for a manifold equipped with a spectral network, we construct equivalencesbetween chern-simons invariants of flat over and chern-simons invariants of flat overramified double covers applications include a new viewpoint on dilogarithmic formulas for chern-simons invariants of flat over triangulated 3-manifolds, and an explicit description of chern-simons lines of flat over triangulated surfaces.