On Gauge Equivalence of Tachyon Solutions in Cubic Neveu-Schwarz String Field Theory

Simple analytic solution to cubic Neveu-Schwarz String Field Theory including the $GSO(-)$ sector is presented. This solution is an analog of the Erler-Schnabl solution for bosonic case and one of the authors solution for the pure $GSO(+)$ case. Gauge transformations of the new solution to others known solutions for the $NS$ string tachyon condensation are constructed explicitly. This gauge equivalence manifestly supports the early observed fact that these solutions have the same value of the action density.