We study theoretically the kinetic characteristics (magnetoresistance, Hall field, thermoelectric field) of layered conductors with a multi-sheeted Fermi surface (FS) under conditions of Lifshitsz topological transition, when the topology of the FS may change under the external influence on the conductor, such as pressure or doping impurity atoms. On the example of the Fermi surface consisting of a cylinder and two planes, slightly corrugated along the projection of the momentum along the normal to the layers, we perform analysis of the dependence of the kinetic coefficients on the strong magnetic field Н, when the cyclotron frequency of the conduction electrons is much higher than the frequency of collisions 1/. In the vicinity of the topological transition, when the distance between the various cavities (sheets) of the Fermi surface becomes small, the electron can be moved from one sheet of FS to another with probability due to magnetic breakdown, and its trajectory in a magnetic field becomes complicated and confused. In this way the quadratic increase with a magnetic field of the resistance to the electric current across the layers in the absence of a magnetic breakdown (w=0) is changed by a linear dependence on H when . At the linear growth of the interlayer resistance with H reaches saturation. Hall field essentially depends on the probability of magnetic breakdown, but its asymptote in the collisionless limit is independent on for all values of w. At the quasi-planar sheets of the Fermi surface touch the corrugated cylinders, and with the further action of the perturbation on the conductor there is a break of flat sheet along the line of contact. As a result separate sections of a flat sheet of FS together with the cut halves of the corrugated cylinder form finally the new corrugated cylinder, thus the sign of charge carriers changes. This is not the only way of Lifshitz topological transition, and the study of the Hall and the Nernst-Ettingshausen effects will provide additional important information about the nature of changes in the topological structure of the electron energy spectrum under the phase transition.