To study the viscoelastic properties of certain complex fluids which are described in terms of a multiconnected transient network, we have developed a convenient model system composed of microemulsion droplets linked by telechelic polymers. The phase behavior of such systems has two characteristic features: a large monophasic region which consists of two subregions (a fluid sol phase and a viscoelastic gel phase) separated by a percolation line and a two-phase region at low volume fraction with separation into a dilute sol phase and a concentrated gel phase. From the plausible origin of these features we expect them to be very similar in different systems. We describe here the phase behavior of four different systems we prepared in order to vary the time scale of the dynamical response of the transient network: they consist of the combination of two oil (decane) in water microemulsions differing by the stabilizing surfactant monolayer (cetylpyridinium chloride/ octanol or TX100/TX35) and of two telechelic polymers which are end-grafted poly(ethylene oxide) chains, differing by the end-grafted hydrophobic aliphatic chains C12H25 or C18H37). We first summarize the characterization of the structure of the four systems by small angle neutron scattering: the size of the microemulsion droplets is found to be constant in a given system upon addition of a telechelic polymer. In the CPCl systems we find a mean radius of the microemulsion droplets of 62 +/- 1 Angstrom and a very narrow size distribution, and in the TX systems we find a mean radius of 84 +/- 2 Angstrom and a somewhat larger size distribution. We can then calculate precisely the number of polymers per microemulsion droplet and compare the phase behavior of the four systems in consistent units. As expected, we find very similar phase behavior in the four systems.