We consider the structure of the finite motion sets surrounding the stable periodic orbits in general three-body problem. We study the vicinities of three periodic orbits (von Schubart's orbit in the rectilinear problem, Broucke's orbit in the isosceles one, "Eight" orbit) in non-hierarchical triple systems. These three orbits have the special feature that sometimes one body passes through the center of mass of the triple system. Corresponding triple systems have zero angular momentum. The "Eight" orbit has an intermediate position between two other orbits which are the limiting cases. We have found a "bridge" of long-term metastable systems connecting these three orbits. The metastable trajectories can "stick" to the vicinity of one of the periodic orbits and sometimes shift from one vicinity to another one. The hierarchical Hill-type periodic orbits are also studied and their vicinities are outlined. The structure of near-periodic motion manifold is described.