  We consider a model-independent approach to constrain the equivalence
redshift, $z_{eq}$, at which dark energy and the total matter (cold dark matter
and baryonic) equate their magnitudes. To this aim, in the context of a
homogeneous and isotropic universe, we first consider a generic model where the
dark energy contribution is provided by an unknown function of barotropic
fluids. Afterwards, we compute the deceleration and jerk parameters, evaluating
at our epoch, namely $z=0$, and at $z=z_{eq}$. Thus, by Taylor expanding around
current time the Hubble rate, luminosity and angular distances, we substitute
the theoretical expressions obtained from the aforementioned generic dark
energy model, defining a correspondence between quantities evaluated at $z=0$
and $z=z_{eq}$. In so doing, we directly fit these quantities by means of
current data sets, involving the most recent Pantheon type Ia supernovae,
baryonic acoustic oscillation and Hubble rate points. We consider two
hierarchies in our fitting procedures and compare our findings in the
spatially-flat universe first and including spatial curvature, later. We assess
constraints on the overall equation of state of the universe and its first
derivative. We compare our results with those predicted by the standard
$\Lambda$CDM paradigm. Specifically, our findings are in agreement at the
2$\sigma$ confidence level, assuming a constant dark energy term. However, our
analysis does not rule out the possibility of a slight evolution of dark
energy, indicating a small deviation from the scenario of a pure cosmological
constant. In particular, the possible departures appear consistent with a
phenomenological $\omega$CDM model, rather than more complicated dark energy
parameterizations.
