  Based on General Relativity (GR) we consider two different cosmological
scenarios in where reconstruct the energy exchange (Q) between cold dark matter
(DM) fluid and dark energy (DE) fluid, which is modelled with a DE varying
equation of state (EoS) parameter {\omega}. We here investigate the main
cosmological effects on the growth rate of matter density perturbations
(f{\sigma}8), on the effective Hubble friction term (Heff ), on the effective
Newton constant (Geff ) and on the growth index of the linear matter
fluctuations ({\gamma}). Our study demonstrates that in the coupled models the
evolution of these quantities are modified with respect to the predictions in
the uncoupled models, and therefore could be used to distinguish among coupled
DE scenarios. Finally, we also perform a combined statistical analysis using
current observational data (geometric and dynamical probes) to put more
stringent constraints on the parameters space of the cosmic scenarios studied.
