  For a continuous map on the unit interval or circle, we define the
bifurcation set to be the collection of those interval holes whose surviving
set is sensitive to arbitrarily small changes of their position. By assuming a
global perspective and focusing on the geometric and topological properties of
this collection rather than the surviving sets of individual holes, we obtain a
novel topological invariant for one-dimensional dynamics.
  We provide a detailed description of this invariant in the realm of
transitive maps and observe that it carries fundamental dynamical information.
In particular, for transitive non-minimal piecewise monotone maps, the
bifurcation set encodes the topological entropy and strongly depends on the
behavior of the critical points.
