  We study when two projective bundles over two arbitrary smooth projective
varieties of different dimensions can be isomorphic. We show that two
multi-projective bundles (fibre product of projective bundles) over different
projective spaces cannot be isomorphic, except in the trivial case. We also
give necessary and sufficient conditions for the top varieties of two height 3
towers of projective bundles being isomorphic, under certain assumptions.
