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We solve the Leggett equations for the BCS - BEC crossover in the threedimension resonance p-wave superfluid with the symmetry of the A1 - phase. Wecalculate the sound velocity, the normal density, and the specific heat for theBCS-domain (\mu > 0), BEC-domain (\mu < 0), and close to important point \mu =0 in 100% polarized case. We find the indications of quantum phase - transitionclose to the point \mu(T = 0) = 0. Deep in the BCS and BEC-domains thecrossover ideas of Leggett and Nozieres, Schmitt-Rink work pretty well. Wediscuss the spectrum of orbital waves, the paradox of intrinsic angularmomentum and complicated problem of chiral anomaly in the BCS A1 - phase at T =0. We present two different approaches to a chiral anomaly: one based onsupersymmetric hydrodynamics, another one on the formal analogy with the Diracequation in quantum electrodynamics. We evaluate the damping of nodal fermionsdue to different decay processes in superclean case at T = 0 and find that weare in a ballistic regime \omega\tau >> 1. We propose to use aerogel ornonmagnetic impurities to reach hydrodynamic regime \omega\tau<< 1 at T = 0. Wediscuss the concept of the spectral flow and exact cancellations betweentime-derivatives of anomalous and quasiparticle currents in the equation forthe total linear momentum conservation. We propose to derive and solve thekinetic equation for the nodal quasiparticles both in the hydrodynamic and inthe ballistic regimes to demonstrate this cancellation explicitly. We brieflydiscuss the role of the other residual interactions different from damping andinvite experimentalists to measure the spectrum and damping of orbital waves inA-phase of 3He at low temperatures.

BCS - BEC crossover and quantum hydrodynamics in p-wave superfluids with a symmetry of the A1 - phase