  Topology-changing transitions between vacua of different effective
dimensionality are studied in the context of a 6-dimensional Einstein-Maxwell
theory. The landscape of this theory includes a $6d$ de Sitter vacuum ($dS_6$),
a number of $dS_4 \times S_2$ and $AdS_4 \times S_2$ vacua, and a number of
$AdS_2 \times S_4$ vacua. We find that compactification transitions $dS_6 \to
AdS_2 \times S_4$ occur through the nucleation of electrically charged black
hole pairs, and transitions from $dS_6$ to $dS_4 \times S_2$ and $AdS_4 \times
S_2$ occur through the nucleation of magnetically charged spherical black
branes. We identify the appropriate instantons and describe the spacetime
structure resulting from brane nucleation.
