Galaxy pairs may represent a way station in the evolutionary path from poor groups to giant isolated ellipticals (or fossil groups). To test this evolutionary scenario, we investigated the environment of 4 galaxy pairs composed of a giant elliptical galaxy and its spiral companion. The pairs are very similar from the optical and dynamical point of view, but have very different X-ray properties. The faint galaxy population around the pairs was observed with VIMOS on the VLT. These observations show that the presence of extended diffuse X-ray emission from an IGM is not necessarily connected to the presence of a numerous faint galaxy population. The study of luminosity functions (LFs) indicate that our X-ray luminous pairs are more dynamically evolved than a sample of poor groups with comparable X-ray luminosities from the literature. However, our X-ray faint pairs resemble the LF of those X-ray bright groups and may represent a phase in the dynamical evolution of these groups, where the recent or ongoing interaction, in which the pair E is involved, has destroyed or at least decreased the luminosity of the IGM. The X-ray faint groups LF is also consitent with their evolution into a fossil group.