Kinetic arrest in colloidal dispersions with isotropic attractive interactions usually occurs through the destabilization of the homogeneous phase and the formation of a non-equilibrium network of jammed particles. Theory and simulations predict that a different route to gelation should become available when the valence of each colloidal particle is suitably reduced. Under these conditions, gelation should be achievable through a reversible sequence of equilibrium states. Here we report the reversible dynamic arrest of a dispersion of DNA-based nanoparticles with anisotropic interactions and a coordination number equal to four. As the temperature is decreased, the relaxation time for density fluctuations slows down by about five orders of magnitude, following an Arrhenius scaling in the entire experimentally accessible temperature window. The system is in thermodynamic equilibrium at all temperatures. Gelation in our system mimics the dynamic arrest of networking atomic strong glass formers such as silica, for which it could thus provide a suitable colloidal model.