In this contribution we present a brief overview of recent results about the effects of electron-phonon interaction in electronic transport through metallic single-walled carbon nanotubes. In particular, we present an electron-phonon-induced backscattering mechanism which can be seen as the removal of degeneracies in the electron-phonon Fock space. This mechanism, which is activated when driving the system out of equilibrium, is beyond the scope of commonly used mean field approaches. Possible experimental consequences of such phenomenon are also discussed.