I can visually compare the alignments
IGV displays all alignments _relative to the reference genome_. The x axis in IGV is always reference genome coordinates. IGV will never display a read that is not aligned to the reference genome.
I have two sets of alignments from different sequencing runs that I want to compare in IGV ... I want to maintain the order of the read alignments between the two bams so I can visually compare the alignments
Firstly, read names are unique. Secondly if you have performed two different sequencing runs, you have sequenced a different set of DNA fragments in each run. There is not a one-to-one correspondence of reads between sequencing runs. In fact, the only time the two runs will sequence the 'same' thing is when they sequence different PCR duplicates of the same source molecule from the same library prep - something that you can neither tell has happen (exception: you could sequence a single cell), nor want (you want your PCR duplicate rate as low as possible when sequencing).