This paper reports the results of an experimental study of electronic topological transitions in bismuth glass-covered wires doped with acceptor (Sn) and donor (Te) impurities. The temperature dependences of the thermoelectric power and resistance are measured within the temperature range from 1.5 to 300 K and magnetic fields up to 14T. The position of the Fermi level ε_F and the concentration of charge carriers at doping are estimated from the Shubnikov de Haas (SdH) oscillations which are clearly visible from both L electrons and L and T holes in all crystallographic directions. We demonstrate anomalies in the temperature dependences of the thermopower in Bi wires doped with acceptor (Sn) and donor (Te) impurities in the form of a triple (doping by Sn) and double (doping by Te) change in the sign of the thermopower. The effect is interpreted with relation to the manifestation of impurity Lifshitz topological transitions. The SdH oscillation method was used to determine the energy position of the Σ band by doping Bi wires with the acceptor impurity Sn and the T band conduction by doping with Te. It is shown that the appearance of the Σ and T bands in Bi wires doped with the acceptor and donor impurities is responsible for the anomalies in the diffusive thermoelectric power, which gives a good conform with to the theoretical models and predictions.