  The papers by Janszky and Adam [Phys. Rev. A {\bf 46}, 6091 (1992)] and Chen
\textit{et al.} [Phys. Rev. Lett. {\bf 104}, 063002 (2010)] are examples of
works where one can find the following equivalences: belonging to the following
class: quantum harmonic oscillators subjected to different time-dependent
frequency modulations, during a certain time interval $\tau$, exhibit exactly
the same final null squeezing parameter ($r_f=0$). In the present paper, we
discuss a more general case of squeezing equivalence, where the final squeezing
parameter can be non-null ($r_f\geq0$). We show that when the interest is in
controlling the forms of the frequency modulations, but keeping free the choice
of the values of $r_f$ and $\tau$, this in general demands numerical
calculations to find these values leading to squeezing equivalences (a
particular case of this procedure recovers the equivalence found by Jansky and
Adams). On the other hand, when the interest is not in previously controlling
the form of these frequencies, but rather $r_f$ and $\tau$ (and also some
constraints, such as minimization of energy), one can have analytical solutions
for these frequencies leading to squeezing equivalences (particular cases of
this procedure are usually applied in problems of shortcuts to adiabaticity, as
done by Chen \textit{et al.}). In this way, this more general squeezing
equivalence discussed here is connected to recent and important topics in the
literature as, for instance, generation of squeezed states and the obtaining of
shortcuts to adiabaticity.
