  In this paper we generalize the notion of $n$-equivalence relation introduced
by Chen et al. in \cite{Chen2014} to classify constacyclic codes of length $n$
over a finite field $\mathbb{F}_q$, where $q=p^r$ is a prime power, to the case
of skew constacyclic codes without derivation. We call this relation
$(n,\sigma)$-equivalence relation, where $n$ is the length of the code and $
\sigma$ is an automorphism of the finite field. We compute the number of
$(n,\sigma)$-equivalence classes, and we give conditions on $ \lambda$ and
$\mu$ for which $(\sigma, \lambda)$-constacyclic codes and $(\sigma,
\lambda)$-constacyclic codes are equivalent with respect to our
$(n,\sigma)$-equivalence relation. Under some conditions on $n$ and $q$ we
prove that skew constacyclic codes are equivalent to cyclic codes. We also
prove that when $q$ is even and $\sigma$ is the Frobenius autmorphism, skew
constacyclic codes of length $n$ are equivalent to cyclic codes when
$\gcd(n,r)=1$. Finally we give some examples as applications of the theory
developed here.
