  An aim of this article is to highlight dynamical differences between the
greedy, and hence the lazy, $\beta$-shift (transformation) and an intermediate
$\beta$-shift (transformation), for a fixed $\beta \in (1, 2)$. Specifically, a
classification in terms of the kneading invariants of the linear maps
$T_{\beta,\alpha} \colon x \mapsto \beta x + \alpha \bmod 1$ for which the
corresponding intermediate $\beta$-shift is of finite type is given. This
characterisation is then employed to construct a class of pairs
$(\beta,\alpha)$ such that the intermediate $\beta$-shift associated with
$T_{\beta, \alpha}$ is a subshift of finite type. It is also proved that these
maps $T_{\beta,\alpha}$ are not transitive. This is in contrast to the
situation for the corresponding greedy and lazy $\beta$-shifts and
$\beta$-transformations, for which both of the two properties do not hold.
