This appears to be one of those words in flux, as different spellings and punctuation rules are followed by different reputable sources.

Start-up works as a noun (a start-up business), verb (“Start-up the car!”), and adjective (start-up costs), according to merriam-webster.com. The Chicago Manual of Style, which is commonly used in book publishing, agrees.

The Associated Press Stylebook, however, dispenses with the hyphen. So almost all American newspapers and magazines use startup.

And while both oxforddictionaries.com and dictionary.cambridge.org list start-up, they also acknowledge that startup is an acceptable alternative spelling.

No one, however, gives start up as acceptable.

Bottom line: Stick with start-up unless you know the publishing house handling your manuscript uses Associated Press style, then go with startup.