Given two Hamiltonians H_1 and H_2, it may be possible to continuously deform H_1 into H_2 while maintaining the symmetry constraint and gap (that is, there exists continuous function H(t, \vec{k}) such that for all 0 \le t \le 1 the Hamiltonian has no zero eigenvalue and symmetry condition is maintained, and H(0, \vec{k} ) = H_1( \vec{k}) and H(1, \vec{k} ) = H_2( \vec{k})). Then we say that H_1 and H_2 are equivalent.
