-i have 3 group of RNAseq samples, let's call them group A, B, and C.

-i have performed DESEQ on A vs C, and B vs C.

-then I look at the shared DEGs between both comparisons and make conclusions based on the shared DEGs.

since the comparisons "A vs C" and "B vs C" are not independent (because they both involve group C), does this introduce bias when comparing the DEGs identified in both comparisons?

Are you thinking about a specific scenario? If so, can you provide more info? I think the basic answer is that, yes, your choice of group C will influence the DEGs you get from A-vs-C and B-vs-C. I don't think this consitututes "bias", however, at least in the sense of bias as a consistent difference from a true value.

Note that by basic algebra A vs C and B vs C is the same as A vs B, so you might rethink your analysis to answer your question in a much simpler way.