Detailed studies of the azimuthal dependence of the mean fragment and flow energies in the Au+Au and Xe+CsI systems are reported as a function of incident energy and centrality. Comparisons between data and model calculations show that the flow energy values along different azimuthal directions could be viewed as snapshots of the fireball expansion with different exposure times. For the same number of participating nucleons more transversally elongated participant shapes from the heavier system produce less collective transverse energy. Good agreement with BUU calculations is obtained for a soft nuclear equation of state. 25.75.Ld;25.70.Pq One of the main motivations to study heavy ion collisions at high energy is to obtain information on the equation of state (EoS) for nuclear matter under conditions of pressure and temperature different from those in normal nuclei. The search for hot and dense nuclear matter created in such collisions is confronted with dynamical consequences of the high incident energy necessary to reach such conditions and with the difficulty to reach a thermal equilibrium in finite systems. Dynamical aspects refer not only to the initial phase of the collision, but also to the evolution stage of the formed fireball. Thus, detailed experimental information on the expansion dynamics is required. The simplest situation corresponds to central collisions with the advantage of the azimuthal symmetry and of the lack of spectator matter. Predicted in early seventies [1,2], the collective expansion of the hot and dense fireball produced in central collisions was evidenced experimentally [3][4][5][6][7][8][9][10][11]. Although central collisions seem to deliver the cleanest signal on the collective expansion on first sight, two issues are worth mentioning: i) While the axial symmetry of the dynamical evolution holds, the spherical symmetry has to be inspected. Preequilibrium emission and transparency effects could influence the spherical symmetry of the expanding system. ii) With regard to reaching pressure, the nuclear matter, not being confined in transverse directions, can escape freely in any direction perpendicular to the collision axis starting from the very first moments of the collision. For reduced centrality, other complications appear. One has to deal with rotating expanding objects in the presence of spectator matter. Nevertheless there are also some advantages in studying less central collisions: i) rotation and shadowing can be used as internal clocks for getting deeper information on the expansion dynamics, ii) the centrality can be used to control the shape and content of the fireball and of the shadowing matter, iii) for a given centrality the passage time of the shadowing objects can be controlled varying the incident energy, iv) the confinement of the spectators becomes more efficient in transverse directions than in the central collisions. Symmetry considerations imply two dominant components in the particle transverse emission: azimuthally symmetric emission and an elliptic mo...