  A homogeneous roof is a rational homogeneous variety of Picard rank 2 and
index $r$ equipped with two different $\mathbb P^{r-1}$-bundle structures. We
consider bundles of homogeneous roofs over a smooth projective variety,
formulating a relative version of the duality of Calabi--Yau pairs associated
to roofs of projective bundles. We discuss how derived equivalence of such
pairs can lift to Calabi--Yau fibrations, extending a result of Bridgeland and
Maciocia to higher-dimensional cases. We formulate an approach to prove that
the $DK$-conjecture holds for a class of simple $K$-equivalent maps arising
from bundles of roofs. As an example, we propose a pair of eight-dimensional
Calabi--Yau varieties fibered in dual Calabi--Yau threefolds, related by a GLSM
phase transition, and we prove derived equivalence with the methods above.
