We present a multi-epoch (20 years baseline) kinematical investigation of HH52, 53, and 54 at optical and near-IR wavelengths, along with medium and high- resolution spectroscopic analyses, probing the kinematical and physical time variability conditions of the gas along the flows. By means of multi-epoch and multi-wavelength narrow-band images, we derived proper motions, tangential velocities, velocity and flux variability of the knots. Radial velocities and physical parameters of the gas were derived from spectroscopy. Finally, spatial velocities and inclination of the flows were obtained by combining both imaging and spectroscopy. The P.M. analysis reveals three distinct, partially overlapping outflows. In 20 years, about 60% of the knots show some degree of flux variability. Our set of observations apparently indicates acceleration and deceleration in a variety of knots along the jets. For about 20% of the knots, mostly coincident with working surfaces or interacting knots along the flows, a relevant variability in both flux and velocity is observed. We argue that both variabilities are related and that all or part of the kinetic energy lost by the interacting knots is successively radiated. The analysis indicates the presence of very light, ionised, and hot flows, impacting a denser medium. Several knots are deflected. At least for a couple of them (HH54 G and G0), the deflection originates from the collision of the two. For the more massive parts of the flow, the deflection is likely the result of the flow collision with a dense cloud or with clumps.
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