Thanks to the widespread availability of large-scale datasets on scholarly outputs, science itself has come under the microscope with the aim of capturing a quantitative understanding of its workings. In this study, we leverage well-established cognitive models coming from anthropology in order to characterise the personal network of collaborations between scientists, i.e., the network considered from the standpoint of each individual researcher (referred to as ego network), in terms of the cognitive investment they devote to the different collaborations. Building upon these models, we study the interplay between the structure of academic collaborations, academic performance, and academic mobility at different career stages. We take into account both purely academic mobility (i.e., the number of affiliation changes) and geographical mobility (i.e., physical relocations to different countries). For our investigation, we rely on a dataset comprising the geo-referenced publications of a group of 81,500 authors extracted from Scopus, one of the biggest repositories of academic knowledge. Our main finding is that there is a clear correlation between the structure of co-authorship ego networks and academic performance indices: the more one publishes and the higher their impact, the larger their collaboration network. However, we observe a capacity bound effect, whereby, beyond a certain point, higher performances become increasingly less correlated with large collaboration networks. We also find that international academic migrants are better at growing their networks than researchers that only migrate within the same country, but the latter seem to be better in exploiting their collaboration to achieve higher impact. High academic mobility does not appear to translate into better academic performance or larger collaboration networks.