Abstract
In this paper, the relationships among the instantaneous invariants of a one-parameter Lorentzian spatial movement and the local invariants of the axodes are studied. New proofs for Euler-Savary, and Disteli formulae are given which demonstrate the elegance and efficiency of the E. Study map in Lorentzian spatial kinematics. Consequently, two spacelike line congruences are introduced and their spatial equivalent are examined in detail.