  We address three genuine phantom dark energy models where each of them
induces the particular future events known as Big Rip, Little Rip and Little
Sibling of the Big Rip. The background models are fully determined by a given
dark energy equation of state. We first observationally constrain the
corresponding model parameters that characterise each paradigm using the
available data of supernova type Ia, Cosmic Microwave Background and Baryonic
Acoustic Oscillations by using a Markov Chain Monte Carlo method. The obtained
fits are used to solve numerically the first order cosmological perturbations.
We compute the evolution of the density contrast of (dark) matter and DE, from
the radiation dominated era till a totally DE dominated universe. Then, the
obtained results are compared with respect to $\Lambda$CDM. We obtain the
predicted current matter power spectrum and the evolution of $f\sigma_8$ given
by the models studied in this work. Finally, the models are tested by computing
the reduced $\chi^2$ for the `Gold2017' $f\sigma_8$ dataset.
