I didn't say enything
To prove the homeomorphism you need to find function f:A->B with following properties Homomorphism - Wikipedia, the free encyclopedia.
In your case you have 2 intervals [a1,b1] & [a2,b2]. You can make such function by stretching one interval and then move it to the beginning of the second one.
-------[a1............b1]----------
------------[a2...........b2]------