In American English, blowup is one word when it functions as a noun meaning (1) an explosion (usually figurative), (2) an outburst of temper, (3) an enlargement of a photograph, and (4) a collapse in performance (especially in sports). It also works as a modifier for items that are inflated with air—for example, blowup doll, blowup bed. The two-word blow up is the verb meaning (1) to explode, (2) to inflate, or (3) to lose one’s temper. Blowup never works as a verb. Blown up, blew up, blows up, and blowing up are always two words.
In British and Australian English, most publications use the hyphenated blow-up for the noun and verb senses. Blowup is a little more common in Canadian publications, but they generally favor blow-up as well.
Examples
For example, these major American publications have no qualms about making blowup one word:
We don’t know whether a Chinese blowup is around the corner or not. [Forbes]
Following a public blowup at the 2007 World Cup, … Solo bounced back at the 2008 Olympics … [Sports Illustrated]
Another section of the farm contains several blowup bouncers and water slides … [New York Daily News]
Blow-up is usually preferred in non-U.S. publications—for example:
Instead, Australian consumers and voters have been spooked … by a Greek sovereign debt default or a US debt and dollar blow-up. [The Australian]
Charl Schwartzel, who won the Masters in April after McIlroy’s final-round blow-up, closed solidly for a three-under 69 … [Toronto Star]
A student who put a blow-up sex doll in the toilets at his high school faces a potential eight years in jail … [Daily Mail]
And of course, blow up should always be two words when it functions as a verb—for example:
The summer blockbuster season always serves as an unwritten invitation for filmmakers to blow up stuff. [Washington Post]
Greece could blow up at any moment … [Telegraph]

