We develop a formalism to model neutrino evolution encompassing both flavor and particle-antiparticle mixings and decohering collisions. Our results include a quantum kinetic equation (a set of coupled scalar equations) for the generalized neutrino density matrix, valid for arbitrary neutrino masses and kinematics, and a comprehensive set of Feynman rules to compute collision integrals for coherently evolving states. We expose a novel shell structure describing the phase space of mixing neutrinos and show how the prior information on the system can enter into the theory and modify the neutrino flavor evolution. Potential applications of our results include modelling neutrino distributions in hot and dense environments and studies of neutrino mixing effects in colliders and in the early Universe.