Substantial collective flow is observed in collisions between Lead nuclei at LHC as evidenced by the azimuthal correlations in the transverse momentum distributions of the produced particles. Our calculations indicate that the Global v1-flow, which at RHIC peaked at negative rapidities (named as 3rd flow component or anti-flow), now at LHC is going to turn toward forward rapidities (to the same side and direction as the projectile residue). Potentially this can provide a sensitive barometer to estimate the pressure and transport properties of the Quark-Gluon Plasma. Our calculations also take into account the initial state Center of Mass rapidity fluctuations, and demonstrate that these are crucial for v1 simulations. In order to better study the transverse momentum flow dependence we suggest a new "symmetrized" v1S flow component; and we also propose a new method to disentangle Global v1 flow from the contribution generated by the random fluctuations in the initial state. This will enhance the possibilities of studying the collective Global v1 flow both at the STAR Beam Energy Scan program and at LHC.