We prove that the vanishing spheres of the Lefschetz pencils
constructed by Donaldson on symplectic manifolds of any dimension are
conjugated under the action of the symplectomorphism group of the
fiber. More precisely, a number of generalized Dehn twists may be used
to conjugate those spheres. This implies the non-existence of
homologically trivial vanishing spheres in these pencils. To develop
the proof, we discuss some basic topological properties of the space
of asymptotically holomorphic transverse sections.