It was shown for the first time in  that neutrino spin (or spin-flavor) precession can be engendered not only by neutrino interaction with the transversal magnetic field but also by neutrino interaction with matter in the case when there is a transversal matter current or matter polarization. The generalized Bargmann-Michel-Telegdi equation [2-4] for description of the neutrino spin evolution in moving matter was used in .
Recently the effect of neutrino spin precession in transversally moving matter
has attracted reasonable interest within studies of neutrino fluxes from supernovae [5-8]. In  we have demonstrated a consistent derivation of the effect of the neutrino spin and spin-flavor oscillations in the transversal matter currents based on the direct calculation of the neutrino evolution effective Hamiltonian. In the proposed presentation we continue this line and present a regroups derivation of neutrino spin and spin-flavor evolution effective Hamiltonians accounting for effects of neutrino vacuum mixing, neutrino mass states interaction with a constant magnetic field (the transversal and longitudinal components) with a particular focus on effects of neutrino flavour interactions with matter transversal and longitudinal currents. The neutrino spin and spin-flavor oscillation probabilities are obtained for different cases that are of interest for astrophysical applications.
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 A.Lobanov, A.Studenikin, Neutrino oscillations in moving and polarized matter under the influence of electromagnetic fields, Phys.Lett. B515 (2001) 94.
 A. Studenikin, Neutrino spin and spin-flavour oscillations in transversally moving or polarized matter, Journal of Physics: Conference Series 718 (2016) 062076; arXiv: 1610.06563.
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 A. Studenikin, From neutrino electromagnetic interactions to spin
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