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Yeah, all of the Dragon Ball series is anime. They all existed as original comics and animation in Japan long before you could get them at Walmart. Where it gets a little fuzzy, as far as I'm concerned, and what I've generally observed, is when you get into series that might have Western origins contracted out to Japanese animation studios.
GI Joe would be a good example. If memory serves, it was mostly done by the same studios that were also involved with the Transformers, a series that's often confused as somehow "for America" but this isn't the case at all since the original Japanese toys predate the original Star Wars. Just check out the copyright stamped into Optimus Prime, a real, original one, if you have it or are near one at a toy convention. But when I see animation produced by studios like Tokyo Movie Shinsha and Toei, it doesn't get more anime than that, technically speaking.
Other sorta grey area series would be Thundercats, Silverhawks, Spiral Zone, Mighty Orbots and The Galaxy Rangers. I believe most of these also aired in Japan as well as the animation being produced there, whether Western companies were involved in any way, so I still consider them all technically anime. A few of them have additional legitimacy in that a few pop up as "in joke" references in other, purely JDM shows.
Then you have the recent very Western titles animated by very Japanese studios and directors, like Blade, Highlander and Dante's Inferno.