Both are correct. Using "up" emphasizes completeness.
The only thing I would question is "stop". What does it mean to open a "stop"? Do you mean something else? Do you mean "open a shop"?
They're gonna open up another store, I heard.
Here's the phrasal verb "open up" from the
AHD.
open: West's Encyclopedia of American Law (Full Article) from Answers.com
With the underlined examples, it's also correct to use just "open", but it wouldn't sound the same. Sometimes we need "up" to complete the meaning by emphasizing completeness, as in completely opened up.
phrasal verb: open up- To spread out; unfold: A green valley opened up before us.
- To begin operation: The new store opens up next month.
- To begin firing: The artillery opened up at dawn.
- > Informal. To speak freely and candidly: At last the frightened witness opened up and told the truth.
- To make an opening in by cutting: The surgeon opened up the patient's chest.
- To make available or accessible: open up new markets.
- Informal. To accelerate. Used of a motor vehicle.
> This sense of the verb which means speak freely and candidly, requires "up" in order to be correct.
Informal. To speak freely and candidly:
At last the frightened witness opened up and told the truth.