The physical spin program at high $p_T$ region and energies $s^{1/2}_{NN} sim 10 GeV$ is discussed. Its shown that cumulative processes, color transparency problem and polarization phenomenons directly connect with properties new form of the nuclear
matter as Color Quark Condensate(CQC). Studies of CQC one of the most important physical problem and can be realized using polarized ion beams at JINR nuclotron-M (and in future at NICA). The calculations of spin resonance strengthes in the linear approximation for p, d, t and $^3He$ beams in the JINR nuclotron are presented. The methods to preserve the degree of polarization during crossing the spin resonances are examined. The method of matching the direction of polarization vector during the beam injection in to the ring of the nuclotron is given. These methods of spin resonance crossing can be used to accelerate polarized beams in the other cyclic accelerators.
