How to manage multiple job interviews

I'm currently in two jobs selection, one is in a start up with a awesome workplace (pretty informal) and the other one is one of the biggest banks of my country, solid carreer plan and compensation. Both of them are in a advanced level, but what makes me anxious is what should I do if I start to work in the first one and then, days later, I get accepted in the second one? I just hate the idea of "waste their time". Srry for bad english.

usa jobs
usa jobs resume
usa hotel jobs
usajobs
usa jobs federal government
usa job in ksa
usa jobs
usa jobs login
usa jobs gov
usajobs.gov
www.usajobs.gov
usajobs.com
usajobs
usajobs.gov official