Looking on the internet deeply has found these results:

build up is the most popular phrase on the web.

buileing up 122,700,000 results on the web	build up 185,200,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	What we say and do today must serve to build up trust. Try to build up trust, build a relationship. The EU has also helped build up an extremely comprehensive framework of regional, sectoral and general cooperation agreements. We need a talus to build up this here. Finally, we must gradually build up a security and defence identity. He exploited his position to build up his fortune. We are also working to build up the ministries of trade and energy. I worked 26 years of my life to build up that restaurant.

buileing up

122,700,000 results on the web

build up

185,200,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

What we say and do today must serve to build up trust.
Try to build up trust, build a relationship.
The EU has also helped build up an extremely comprehensive framework of regional, sectoral and general cooperation agreements.
We need a talus to build up this here.
Finally, we must gradually build up a security and defence identity.
He exploited his position to build up his fortune.
We are also working to build up the ministries of trade and energy.
I worked 26 years of my life to build up that restaurant.