  In the study of global bifurcations of vector fields on $S^2$, it is
important to distinguish a set "where the bifurcation actually occurs", -- the
bifurcation support. Hopefully, it is sufficient to study the bifurcation in a
neighborhood of the support only.
  The first definition of bifurcation support was proposed by V.Arnold. However
this set appears to be too small. In particular, the newly discovered effect,
an open domain in the space of three-parametric families on $S^2$ with no
structurally stable families, is not visible in a neighborhood of the
bifurcation support.
  In this article, we give a new definition of "large bifurcation support" that
accomplishes the task. Roughly speaking, if we know the topological type of the
phase portrait of a vector field, and we also know the bifurcation in a
neighborhood of the large bifurcation support, then we know the bifurcation on
the whole sphere.
