  We compute the Bieri-Neumann-Strebel invariants $\Sigma^1$ for the
generalized solvable Baumslag-Solitar groups $\Gamma_n$ and their finite index
subgroups. Using $\Sigma^1$, we show that certain finite index subgroups of
$\Gamma_n$ cannot be isomorphic to $\Gamma_{k}$ for any $k$. In addition, we
use the BNS-invariants to give a new proof of property $R_\infty$ for the
groups $\Gamma_n$ and their finite index subgroups.
