  Bundles of matrix pencils (under strict equivalence) are sets of pencils
having the same Kronecker canonical form, up to the eigenvalues (namely, they
are an infinite union of orbits under strict equivalence). The notion of bundle
for matrix pencils was introduced in the 1990's, following the same notion for
matrices under similarity, introduced by Arnold in 1971, and it has been
extensively used since then. Despite the amount of literature devoted to
describing the topology of bundles of matrix pencils, some relevant questions
remain still open in this context. For example, the following two: (a) provide
a characterization for the inclusion relation between the closures (in the
standard topology) of bundles; and (b) are the bundles open in their closure?
The main goal of this paper is providing an explicit answer to these two
questions. In order to get this answer, we also review and/or formalize some
notions and results already existing in the literature. We also prove that
bundles of matrices under similarity, as well as bundles of matrix polynomials
(defined as the set of $m\times n$ matrix polynomials of the same grade having
the same spectral information, up to the eigenvalues) are open in their
closure.
