  We study the dynamical status of the poor, low X-ray luminous galaxy clusters
Abell 610, Abell 725, and Abell 796 (at z=0.1, 0.09, and 0.16, respectively),
containing diffuse radio sources (relic, relic, and possible halo,
respectively). Our analysis is based on new spectroscopic data obtained at the
William Herschel Telescope for 158 galaxies, new photometry obtained at the
Isaac Newton Telescope with the addition of data recovered from the Data
Release 5 of the Sloan Digital Sky Survey. We use statistical tools to select
57, 36, and 26 cluster members and to analyze the kinematics of cluster
galaxies, as well as to study the 2D cluster structure. The low values we
compute for the global line-of-sight velocity dispersion of galaxies (420-700
km/s) confirm that these clusters are low-mass clusters. Abell 610 shows a lot
of evidence of substructure. It seems to be formed by two structures separated
by about 700 km/s in the cluster rest-frame, having comparable velocity
dispersion (about 200 km/s) and likely causing a velocity gradient. The
analysis of the 2D galaxy distribution shows a bimodal distribution in the core
elongated in the SE-NW direction. Abell 725 and Abell 796, which are less
sampled, show marginal evidence of substructure in the velocity space. They are
elongated in the 2D galaxy distribution. For both Abell 610 and Abell 725 we
shortly discuss the possible connection with the hosted diffuse radio relic.
Our results show that relic radio sources are likely connected with merger
events,but are not limited to massive clusters. About the possible halo source
in Abell 796, there is some evidence of a merger event in this non-massive
cluster, but a pointed radio observation is necessary to confirm this halo.
