Re-entering USA multiple times in a month using a B1/B2 visa

I want to visit USA from Bangladesh using my B1/B2 visa. After exploring the west coast of USA, I want to visit Vancouver in Canada from USA.

After the trip to Canada, I want to return to USA and take a flight to Mexico (flight from LA/LV to Mexico is much much cheaper than Vancouver) after my Canadian trip. Then, from Mexico, I want to enter USA again as my flight to my country is from NY.

To sum up, I will be visiting USA thrice in the span of 5 weeks. Will I face any problem in the immigration?

I have multiple entry visas for both USA and Canada.