  Recent works have explored non-perturbative effects due to the existence of
(infinitesimal) Gribov copies in Yang-Mills-Chern-Simons theories in three
Euclidean dimensions. In particular, the removal of such copies modify the
gauge field propagator by a self-consistent dynamically generated mass
parameter, the Gribov parameter. Due to the interplay with the topological mass
introduced by the Chern-Simons term, the propagator features a non-trivial set
of phases with poles of different nature, leading to the possible
interpretation of a confinfing to deconfining phase transition. Inhere, we
restore the BRST symmetry which is softly broken by the elimination of gauge
copies and provide a BRST-invariant discussion of such a transition. In order
to make clear all physical statements, we deal with linear covariant gauges
which contain a gauge parameter and therefore allow for an explicit check of
gauge parameter independence of physical results. We also discuss the
generation of condensates due to the infrared relevance of infinitesimal Gribov
copies.
