  We study the $p$-rank stratification of the moduli space
$\mathcal{ASW}_{(d_1,d_2,\ldots,d_n)}$, which represents
$\mathbb{Z}/p^n$-covers in characteristic $p>0$ whose
$\mathbb{Z}/p^i$-subcovers have conductor $d_i$. In particular, we identify the
irreducible components of the moduli space and determine their dimensions. To
achieve this, we analyze the ramification data of the represented curves and
use it to classify all the irreducible components of the space.
  In addition, we provide a comprehensive list of pairs
$(p,(d_1,d_2,\ldots,d_n))$ for which $\mathcal{ASW}_{(d_1,d_2,\ldots,d_n)}$ in
characteristic $p$ is irreducible. Finally, we investigate the geometry of
$\mathcal{ASW}_{(d_1,d_2,\ldots,d_n)}$ by studying the deformations of cyclic
covers which vary the $p$-rank and the number of branch points.
