Many Websites provide such user-friendly service for free , to check any yahoo e-mail status whether ( Online , Busy or Invisible )
Top 10 Websites ( Ranked by Google Search Engine) :-
1- Yahoo Status
2- Detect invisible
3- ImVisible
4- Status Detect
5- Jdetector
6- YmLooK
7- YAHOO-STATUS
8- Yahoo Check Invisble
9- Block Status
10- 4 Invisible