Does B1 Visa application automatically cancels H1-B Visa?


I am working with company A and my H1B Visa is stamped. The stamp is expiring in Sep 2014. I have not travelled to US yet.

Now I have got an offer from Company B. They say that they plan to send me to US but they don't want me to travel on H1B Visa. They want to apply B1 Visa for me.

1) Will my H1-B visa automatically get cancelled if I go for B1 also?

2) Can H1-B and B1 be valid together at the same time?

3) Can I travel on my existing H1 B also after my travel on B1?