Does the artisan's level carry through to higher acts?

Before investing a small fortune into levelling up my artisan (currently on act I) I want to know if his level carries through to the next act, otherwise I'll just wait and level him in the last act.

Not only do the Artisans' levels carry through to higher acts, but they're shared across all characters on your account.

The one exception being that Hardcore characters have a separate set of Artisans. But as long as you stick to one "core" (either hard or soft), know that your Artisans will not lose levels when swapping difficulty, character, or act.

Artisans maintain their levels (and any learned recipes) not only across acts, but also across characters (with the exception of hardcore vs normal; artisans leveled by hardcore characters are not accessible to normal characters, and vice versa).

Yes, they carry through. They even carry between difficulties and characters: The artisan levels when you start a new game on nightmare will be the same as where you left it when you finished the game in the lower difficulty.