By 'copy number variation' (CNV), you must mean 'copy number alterations'. Copy number variation is regarded as a form of 'natural' variation in the genome that differs from one individual to the next, much like single nucleotide polymorphisms (SNPs). CNV, much like SNPs, may or may not have an association with healthy or disease phenotypes. However, they (CNV and SNP) are both strictly* part of the germline. Copy number alterations (CNAs) in the context of cancer are regarded as copy number events in the tumour that differ from germline copy number events.
It is actually quite relevant to compare CNA events between tumour stages. Why? More advanced tumour stages are more likely to exhibit chromosomal instabiltiy (CIN) / genomic instability at some level due to somatic mutation in genes whose roles are to maintain the genome healthy. An unstable genome is conducive to a greater number of chromosomal abnormalities, such as CNAs and other structural variants. CIN is also conducive to a heterogeneous tumour population, which may in turn translate into a more aggressive and treatment-resistant tumour (but not always, as it may conversely improve treatment response). So, the study of CNAs in different stages has much clinical relevance and can be a marker of tumour stage and aggressiveness [of the tumour].
An interesting work would be to not only compare CNA events between tumour stages, but to also link these to somatic mutations in CIN signature genes.
As with everything in cancer, there are exceptions, and there are exceptions to all statements that I've made here.
Edit: a tumour exhibiting CIN / genomic instability is likely to contain a very high frequency of CNAs, which may be too difficult to study. Thus, people have turned to instead focusing on the study of recurrent CNA, i.e., CNAs that have a higher than expected frequency in a group of samples, such as Stage IV colon cancer samples. By looking at the recurrent CNA events, we may gain insight into molecular mechanisms within the tumour.