  Based on the effective-mass concept, we perform the Faddeev calculations for
a low-lying spectrum of 3$\alpha$ states in $^{12}$C nucleus. A three-body
potential is used to describe the known breaking of the 3$\alpha$-cluster
structure in the nucleus. We show that the contribution of the three-body
potential to the Hamiltonian can be compensated by increasing/decreasing the
$\alpha$-particle free mass. The effective-mass values are adjusted so that to
reproduce the experimental data for the $^{12}$C nucleus. The energy dependence
of the effective mass and the correlation to a three-body potential are
discussed. We show that the coupling between the $0^+$ ($2^+$) levels forms a
specific picture of anti-crossing on the energy/effective-mass plane.
