  Let $\mathcal B$ be an infinite subset of $\{1,2,\dots\}$. We characterize
arithmetic and dynamical properties of the $\mathcal B$-free set $\mathcal
F_{\mathcal B}$ through group theoretical, topological and measure theoretic
properties of a set $W$ (called the window) associated with $\mathcal B$. This
point of view stems from the interpretation of the set $\mathcal F_{\mathcal
B}$ as a weak model set. Our main results are: $\mathcal B$ is taut if and only
if the window is Haar regular; the dynamical system associated to $\mathcal
F_{\mathcal B}$ is a Toeplitz system if and only if the window is topologically
regular; the dynamical system associated to $\mathcal F_{\mathcal B}$ is
proximal if and only if the window has empty interior; and the dynamical system
associated to $\mathcal F_{\mathcal B}$ has the "na\"ively expected" maximal
equicontinuous factor if and only if the interior of the window is aperiodic.
