I just got my new MacBook Air and want to transfer apps and files from mine Time Capsule backup. Both me and the wife uses the same 2 TB Capsule for daily backup.
I open Migration Assistant and chooses "Time Machine or other disk" and follow the steps. It finds the disk and I enter the password correct. But I only see my wifes backup in Migration Assistant. Not mine. I have turned Time Machine off in my older MBA and I am running the same version of OSX.
MacBook Air, OS X Mountain Lion, 2,13 GHz Intel Core 2 Duo, 4 GB RAM
On the old machine, enter Time Machine and look at the most recent snapshot of the top level of the startup volume. That's the window behind the frontmost window in the time-travel view. Do you see the following folders:
The sollution was simple. I unplugged the Time Capsule and let i restart and both mine and my wifes backup volumes where there. I suppose it was kind of locked to my old computer and hadn't timed out or something like that.