Longitudinal or transverse magnetic fields applied on a crystal of Mn12 acetate allows one to observe independent tunnel transitions between m = -S+p and m = S-n-p ( n = 6-10, p = 0-2 in longitudinal field and n = p = 0 in transverse field). We observe a smooth transition (in longitudinal) from coherent ground-state to thermally activated tunneling. Furthermore, two ground-state relaxation regimes show a crossover between quantum spin relaxation far from equilibrium and near equilibrium, when the environment destroys multimolecule correlations. Finally, we stress that the complete Hamiltonian of Mn12 should contain odd spin operators of low order.