Visualisation of bandwith of filter with sampling
$B$ is the cut-off frequency of the anti-alias filter needed before sampling; $\omega_0$ is the signal bandwidth, and $\omega_s$ is the sampling frequency.

$B$ can also be the cut-off frequency of the (ideal) reconstruction filter (band-limited interpolator).

If this is the case, this suggests that the reconstruction filter is an ideal low-pass filter with cut-off frequency between the signal bandwidth and the next overlapped frequency component ($\omega_s - \omega_0$). The sampled signal contains repetitions of the original specturm every $\omega_s$, so when reconstructing, you want to get rid of all these repetitions and keep only the spectrum centered at 0.

I don't know what literature you are referring to, and why is it so crappy.