  The topological theory of phase transitions has its strong point in two
theorems proving that, for a wide class of physical systems, phase transitions
necessarily stem from topological changes of some submanifolds of configuration
space. It has been recently argued that the $2D$ lattice $\phi^4$-model
provides a counterexample that falsifies this theory. It is here shown that
this is not the case: the phase transition of this model stems from an
asymptotic ($N\to\infty$) change of topology of the energy level sets, in spite
of the absence of critical points of the potential in correspondence of the
transition energy.
