Crossing over occurs between equivalent portions of two nonsister chromatids.
Each chromatid contains a single molecule of DNA. So the problem of crossing over is really a problem of swapping portions of adjacent DNA molecules.
It must be done with great precision so that neither chromatid gains or loses any genes. In fact, crossing over has to be sufficiently precise that not a single nucleotide is lost or added at the crossover point if it occurs within a gene. Otherwise a frameshift would result and the resulting gene would produce a defective product or, more likely, no product at all.
How do nonsister chromatids ensure that crossing over between them will occur without the loss or gain of a single nucleotide? One plausible mechanism for which there is considerable laboratory evidence postulates the following events.
Fig. 8.2.1 DNA Recombination
Note that each recombinant DNA molecule includes a region where nucleotides from one of the original molecules are paired with nucleotides from the other. But no matter. The need for a smooth double helix guarantees that each exchange takes places without any gain or loss of nucleotides. So long as the total number of nucleotides in each strand and the complementarity (A-T, C-G) is preserved, this "heteroduplex" region (which may extend for hundreds of base pairs) will only rarely have genetic consequences.
And these may, in fact, be helpful because the synthesis of a short stretch of DNA using the template provided by the other chromatid also provides a mechanism for repairing any damage that might have been present on the "invading" strand of DNA. If the cut in the molecule 1 occurs in the region of a mutation, the damaged or incorrect nucleotides can be digested away. Refilling the resulting gap, using the undamaged molecule 2 as the template, repairs the damage to molecule 1.
Why should the cutting and ligation be limited to the strands shown? They are not. Half the time the cutting and ligating rejoins the original parental arms. In these cases, no crossover takes place. The only genetic change that might have occurred is a transfer of some genetic information in the heteroduplex region.
So crossing over not only provides a mechanism for genetic recombination during meiosis but also provides a means of repairing damage to the genome.