Bettween was a very useful service that seems to have stopped operating now.
The service let you track Twitter conversation between two accounts.
Twitter itself has been improving in this area but you can only see individual conversations between two accounts.
Bettween on the other hand provided continues interaction between two accounts over a long period of time.
The developers spoke about the decision to shut down the service:
This was always a side project of ours and with its ups and downs we always managed to improve it in little increments. Sadly, we have reached a point where we can no longer take care of it and we have to let it go.
The service of course had no decent revenue model. People were not going to pay for such functionality. Sadly, Twitter does not see any point in offering a similar functionality on their network.