  Consider $(\mathbb{C}^*)^k$ acting on $\mathbb{C}^N$ satisfying certain
'quasi-symmetric' condition which produces a class of toric Calabi-Yau GIT
quotient stacks. Using subcategories of $Coh([\mathbb{C}^N /
(\mathbb{C}^*)^k])$ generated by line bundles whose weights are inside certain
zonotope called the 'magic window', Halpern-Leistner and Sam give a
combinatorial construction of equivalences between derived categories of
coherent sheaves for various GIT quotients. We apply the coherent-constructible
correspondence for toric varieties to the magic windows and obtain a
non-characteristic deformation of Lagrangian skeletons in $\mathbb{R}^{N-k}$
parameterized by $\mathbb{R}^k$, exhibiting derived equivalences between
A-models of the various phases. Moreover, by translating the magic window
zonotope in $\mathbb{R}^k$, we obtain a universal skeleton over $\mathbb{R}^k
\times \mathbb{R}^k \setminus \mathcal{D}$ for some fattening of hyperplane
arrangements $\mathcal{D}$, and we show that the the universal skeleton induces
a local system of categories over $\mathbb{R}^k \times \mathbb{R}^k \setminus
\mathcal{D}$. We also connect our results to the perverse schober structure
identified by \v{S}penko and Van den Bergh.
