Final answer:
The process of pairing non-sister chromatids during prophase I of meiosis for crossing over is called synapsis. It is facilitated by the synaptonemal complex and results in chiasmata, leading to genetic diversity.
Step-by-step explanation:
The pairing of non-sister chromatids along their lengths in prophase I of meiosis, a process that is essential for crossing over, is referred to as synapsis. During synapsis, the homologous chromosomes come together with a precise alignment of genes on the chromatids. This alignment is supported by a structure known as the synaptonemal complex, which facilitates the exchange of genetic material between the chromatids, leading to genetic recombination. This exchange of segments is a crucial event for generating genetic diversity and is observable as chiasmata (singular = chiasma).