1) You create a post to Authorize.net, containing the amount and other assorted fields.
2) Authorize.net processes the transaction, sending back data on the transaction success / fail
3) Your relay response page checks success / fail and generates a URL based on that, passing it back to Authorize.net
4) Authorize.net redirects
5) Your receipt page gives the final message to the customer
Personally, I don't understand why steps 3 and 4 are there, unless it's to mask the success URL, But I didn't program the system. In answer to your question, success / fail is available at step 3 and apparently also at step 5. The data is most likely to be available at step 3 - try logging $response to a text file using print_r (if using PHP) to see what it looks like.
Wish I could be more specific, I've looked at DPM but haven't actually used it yet, since I prefer something slightly more straightforward.