To actually own IPv4 block you need to be a LIR, having only ASN is not sufficient. I don't know much about ARIN, but at RIPE it is pretty expensive to be a LIR. It only makes sense if you have large address space, not for a few /24s.
Discussion
Yes ARIN/RIPE have slightly different rules. I already went through the whole process and am on a waitlist for a /22 via ARIN.
Took only a week or so from start to finish but of course you need a justification and a business.
I believe for RIPE an alternative to being an LIR is to have one sponsor you. I believe IPXO, for example, does this for marketplace customers who want to move to owning address space.