We solve the Leggett equations for BCS-BEC crossover of the resonance p-wave superfluid. We calculate sound velocity, specific heat and the normal density for the BCS-domain (μ > 0), BEC-domain (μ < 0) as well as for the interesting interpolation point (μ = 0) in the triplet A 1 -phase in 3D. We are especially interested in the quasiparticle contribution coming from the zeroes of the superfluid gap in the A 1 -phase. We discuss the spectrum of orbital waves and the superfluid hydrodynamics at

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... mperature T → 0. In this context we elucidate the difficult problem of chiral anomaly and mass-current nonconcervation appearing in the BCS-domain. We present the different approaches to solve this problem. To clarify this problem experimentally we propose an experiment for the measurement of anomalous current in superfluid A 1 -phase in the presence of aerogel for 3 He and in the presence of Josephson tunneling structures for the ultracold gases in magnetic traps. PACS: 67.30.H-Superfluid phase of 3 He; 67.85.Lm Degenerate Fermi gases; 74.20.Rp Pairing symmetries (other than s-wave).