  The resistance of layered conductors with a multisheet Fermi surface (FS), in
a high magnetic field, in the immediate vicinity of Lifshic's topological
transition when the separate FS sheets are drown together by an external
action, pressure in part (and eventual change of the FS connectivity) is
studied theoretically. Analysis of magnetoresistance near topological
transition is illustrated for the case of FS in the shape of lightly corrugated
cylinder and two corrugated planes distributed with a repeated period in the
pulse space. It yields, that as the FS plane sheets approach sufficiently the
cylinder, the charge carriers produce a magnetic breakdown of one FS sheet to
another, decreasing a sharp anisotropy of magnetoresistance to the in-plane
current. Instead of square increase with a magnetic field, the slower
resistance growth remains linear in the field within a broad magnetic-field
range. In the intimate vicinity of topological transition, when the energy gap
between FS layers is negligibly small, the resistance is saturated.
