Once an MVP is on, how long does it take to be sure my start up is successful and go to the next stage? Which number do I need to know it was success?

It depends on what are you testing by launching MVP. MVP is use to run an experiment to test (validate / invalidate) business assumptions (Customer, problem, solution , channel ... assumptions).
If your are interested, I can share some material about MVP and validating business assumptions

If the business makes enough capital to scale up then you're on a right path. The capital may come in the form of revenue or investment. If it comes from revenue then you're absolutely on a right path. If it's investment backed then you're 50% there and much more needs to be done.

Hi...
It is not an exact number. It is what you are measuring..
First: make sure you start to have cash flow and REAL customers
Second: is this cash flow sustainable??
Third: when do you expect to reach a breakeven point? Is your MVP enough? Or future investment is needed? When do you think , based on current customers, you will be able to break even again the new investment?
Fourth: most important thing is Growth.. How do you plan to grow?
By more sales? Or improving efficiency? And is the growth sustainable ?
Is it a constant growth ? Or variable?

Also, reviews from customers and customer satisfaction for your MVP (paying customers) will be your 100% real guide, coz reviews most of the time give you false positives..

Good Luck!

1. MVP is starting point. The first iteration of many to come. Measuring success depends on what your are doing. It could be engagement, users growth, transactions, revenue, etc

2. Listen to your early users and continue to build the product as you get feedback. Make sure whatever you build the customer/user is something they want.