  We analyze B-type D-branes on noncompact toric Calabi--Yau spaces. A general
program is presented to find a set of tilting line bundles that yields the
associated quiver and its relations. In many cases, this set remains fixed as
one moves between phases in the K\"ahler moduli space. This gives a
particularly simple picture of how the derived category remains invariant
across all phases. The combinatorial problems involving local cohomology used
to determine the tilting set are also related to questions of Pi-stability as
one moves between phases. As a result, in some cases precisely those line
bundles in the tilting set remain stable over the whole moduli space in some
sense.
