  The construction of the Bier sphere Bier(K) for a simplicial complex K is due
to Bier. Bj\"orner, Paffenholz, Sj\"ostrand and Ziegler generalize this
construction to obtain a Bier poset Bier(P,I) from any bounded poset P and any
proper ideal I of P. They show shellability of Bier(P,I) for the case where P
is the boolean lattice, and obtain thereby 'many shellable spheres' in the
sense of Kalai. We put the Bier construction into the general framework of the
theory of nested set complexes of Feichtner and Kozlov. We obtain 'more
shellable spheres' by proving the general statement that combinatorial blowups,
hence stellar subdivisions, preserve shellability.
