Flavour effects play an important role in the statistical evolution of particle number densities in several particle and astroparticle physics phenomena. A fully flavour-covariant formulation of transport phenomena is presented, with a Resonant Leptogenesis (RL) scenario in mind, in order to capture all flavour effects, both in the heavy-neutrino and charged-lepton sectors. For concreteness, we consider the Standard Model accompanied by quasi-degenerate heavy Majorana neutrinos, even though the formalism can be easily applied to study flavour effects in other physical situations. Flavour covariance requires one to consider generically off-diagonal number densities, as well as rank-4 rate tensors in flavour space. Particular emphasis is put on the non-trivial generalization of the discrete symmetries C, P and T in the flavour-covariant formalism. The flavour-covariant transport equations provide an unified description of RL, capturing three relevant phenomena: coherent heavy-neutrino oscillations, quantum decoherence in the charged-lepton sector, and the standard resonant CP violation due to heavy-neutrino mixing. We show quantitatively, in a minimal electroweak-scale RL model, that the final asymmetry predicted by the flavour-covariant rate equations is enhanced of even an order of magnitude, as compared to that obtained from flavour-diagonal or partially flavour off-diagonal equations.