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Context . Intermediate-mass protostars can be the preferred targets to study star formation, since they allow us to inquire how the stars form in clustered environments at a relatively close distance from us. Aims . Our aim is to investigate the formation, interaction with the local environment, and propagation of the protostellar jets inside the young stellar object (YSO) cluster G105.42+9.88 (alias LkH α 234). This is one of the least luminous targets of the Protostellar Outflows at the EarliesT Stages (POETS) survey, which has been recently carried out to study young outflow emission on scales of 10–100 au. Methods . We studied the jet launching regions at radii of ≤100 au by employing three different sets of very long baseline interferometry (VLBI) observations of the 22 GHz water masers spanning a time of ≈22 yr. We complemented the VLBI maser data with sensitive multi-band NSF’s Karl G. Jansky Very Large Array (JVLA) continuum observations to image the ionized component of the outflow at scales of 100–1000 au and sensitive Large Binocular Telescope (LBT) H 2 2.12 µm observations to track the jets at scales of 0.1–1 pc. Results . Our combined observations allow us to study the protostellar outflows from the intermediate-mass binary system VLA 3A and 3B, separated by ≈0.″22, and from VLA 2, an intermediate-mass YSO placed ≈1″ to northwest of VLA 3. In each of these three YSOs, the presence of a thermal jet is suggested by previous Very Large Array (VLA) and our JVLA radio continuum observations. Toward VLA 2 the 2001 and 2011 Very Long Baseline Array (VLBA) observations consistently show that the water masers are tracing a compact (size ≈400 au) bipolar collimated (PA ≈ 70°) outflow, i.e., a jet. The analysis of the 3D flow velocities proves that the jet is magneto-centrifugally launched in a magnetohydrodynamic (MHD) disk wind (DW). We infer launch radii in the range 10–50 au for the streamlines traced by the water masers. The global VLBI 2023 water maser observations indicate that the jet propagation can be hindered by a very dense clump placed northeast of VLA 2 and that is consistent with the large-scale LBT H 2 emission, tracing only the southwest lobe of the VLA 2 jet. Instead, the parallel (PA ≈ 55 ° −57 ° ) jets emitted by the nearby YSOs VLA 3A and 3B can be reliably tracked with the H 2 emission at scales of a few 10″ to both the southwest and the northeast. In particular, northeast of VLA 3 the direction of these two jets crosses a linear chain of spaced H 2 knots, which is a clear signature of an episodic jet. In VLA 3B the spatial distribution and intensity of the water masers change significantly between the VLBA 2011 and global VLBI 2023 observations, likely reflecting a different state (active in 2011 and quiescent in 2023) of wind ejection. The variable ejection from VLA 3B could be the origin of the episodic jet observed at larger scales. Conclusions . This work shows that the combination of VLBI observations of the 22 GHz water masers with sensitive high-angular-resolution radio continuum and near-infrared H 2 2.12 µm observations permit to investigate the launching region of protostellar outflows, to trace their interaction with the surrounding environment, and track their paths at larger scales.