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We investigate numerically the transverse versus vortex phase diagram of head-to-head domain walls in Co/Cu/Py spin valve nano-stripes (Py: permalloy), in which the Co layer is mostly single domain while the Py layer hosts the domain wall. The range of stability of the transverse wall is shifted towards larger thickness compared to single Py layers, due to a magnetostatic screening effect between the two layers. An approached analytical scaling law is derived, which reproduces faithfully the phase diagram.