When launching the ASAv in GNS3 by default telnet will partially load and you’ll be welcomed by a blank screen. This has caught me out a few times. The fix is detailed in this excellent blog post.
For posterity to summarise that post. Boot up the ASAv using console type vnc or if you’re on Linux try using spice. Once it’s booted up execute the following command:
ciscoasa#copy disk0:/coredumpinfo/coredump.cfg use_ttyS0
Be careful not to use the letter O it has to be the number 0 at the end of use_ttyS0. Shutdown the ASA, change the console type to Telnet. Power it back on and it should now work.