  Merging galaxy clusters allows to study the different mass components, dark
and baryonic, separately. Also their occurrence enables to test the
$\Lambda$CDM scenario and they could put constrains in the self interacting
cross section of the dark matter particle. It is necessary to perform an
homogeneous analysis of these systems. Hence, based in a recently presented
sample of candidates for interacting galaxy clusters, we present the analysis
of two of these cataloged systems. In this work, the first of a serie devoted
to characterize galaxy clusters in merger process, we perform a weak lensing
analysis of A1204 and A2029/2033 clusters to derive the total masses of each
identified interacting structures together with a dynamical study based on a
two-body model. We also describe the gas and the mass distributions in the
field through a lensing and an X-ray analysis. This is the first of a series of
works which will analyze these type of systems to characterize them. Both
merging clusters candidates do not show evidence of having had a recent merger
event. Nevertheless, there is dynamical evidence that these systems could be
interacting or could interact in the future. It is necessary to include more
constrains in order to improve the methodology to classify merging galaxy
clusters. Characterization of these clusters is important in order to
understand in deep the nature of these systems and their connection with
dynamical studies.
