In Italy, the reversal at the appellate level is considered only a step towards a final decision. It's not considered double-jeopardy because the legal system is set up differently. In the United States though, appeals court ("appellate" is synonymous with "appeals") decisions are weighed equally to trial court decisions in criminal cases. If an appellate court reverses a conviction, the defendant cannot be re-tried because prosecutors in the US cannot appeal criminal cases.

The United States follows US law when making decisions about extradition. This isn't a feature of any specific treaty with Italy: extradition treaties just signify that a country is allowed to extradite. All subsequent extradition requests from those countries are sent through the Department of State for review. Even if it passes review and the person arrested, a court hearing is held in the US to determine whether the fugitive is extraditable. So there are multiple opportunities to look at Italian court procedures and decide whether they count as double-jeopardy under US law. Those investigations would tend toward deciding it does.

Are you saying that the double-jeopardy issue is clear and simple and there is no room for reasonable people to dispute it? If so, how do you explain American law professors who assert that it's not a barrier? Also, would you mind citing the precedent cases which back up your reasoning?

I believe that more likely than not the double-jeopardy issue would be resolved in favor of Knox, but I don't think it's a slam dunk.