  We study the $t{-}V$ disordered spinless fermionic chain in the strong
coupling regime, $t/V\rightarrow 0$. Strong interactions highly hinder the
dynamics of the model, fragmenting its Hilbert space into exponentially many
blocks in system size. Macroscopically, these blocks can be characterized by
the number of new degrees of freedom, which we refer to as movers. We focus on
two limiting cases: Blocks with only one mover and the ones with a finite
density of movers. The former many-particle block can be exactly mapped to a
single-particle Anderson model with correlated disorder in one dimension. As a
result, these eigenstates are always localized for any finite amount of
disorder. The blocks with a finite density of movers, on the other side, show
an MBL transition that is tuned by the disorder strength. Moreover, we provide
numerical evidence that its ergodic phase is diffusive at weak disorder.
Approaching the MBL transition, we observe sub-diffusive dynamics at finite
time scales and find indications that this might be only a transient behavior
before crossing over to diffusion.
