The transverse magnetoconductance of the n-type conductivity InSb whiskers doped by Sn to concentration 4.4 x 10(16) divided by 7.16 x 10(17) cm(-3) were studied in the temperature range 4.2 divided by 70 K and weak magnetic field up to 3 T. The Shubnikov-de Haas oscillations at liquid helium temperature were revealed in the samples with doping concentration corresponding to metal-insulator transition (MIT). The character of transverse magnetoconductance dependences was analysed and compared with theoretical one. The studied magnetoconductance alters its sign for various doping concentration at weak magnetic fields. It is negative and becomes positive for heavily doped samples. Possible mechanisms of the existence of negative and positive magnetoconductance at low temperatures and weak magnetic fields were discussed in the InSb whiskers with doping concentration in the vicinity to MIT. The origin of these effects was connected with the concentration-induced crossover from weak localization to weak antilocalization and explained due to the Rashba spin-orbit interaction in tin doped InSb core-shell wires.