I don't think you understand the difference between a common law and civil law court. This is pretty standard for people who live in NA or the UK.
Knox was never officially found guilty at any point in time. The reason people who don't understand the legal system or the case constantly spout off "double jeopardy" in regard to this case is a result of two factors.
1) Knox was in prison on a Calumny charge for the duration of her first trial. I think many Americans in particular just presumed she was imprisoned on the murder charge - however that was not the case. It just so happened that her sentence was served around the same time her first appeal began in the murder trial giving the illusion that she was released due to an initially successful appeal.
2) In civil law courts and Italy in particular, both the defense AND the prosecution have the right to appeal. The initial finding of the Jury & Judges is never final, in practice 99% of the time the losing side will appeal.
In the first trial, Knox was found guilty. The defense then appealed and secured a new judge (Hellman) to oversee that appeal. Hellman initially declared Knox innocent but the appeal is not finalized until a legal review determines that the trial was conducted appropriately. It was found that Hellman made numerous procedural errors in finding Knox innocent and thus what could be most correlated to a Common Law "mistrial" was applied. Knox was then put through a retrial where she was found guilty and the verdict was upheld upon appeal.
I know that may be confusing, but to put it as simply as possible:
Trial 1: Guilty
Appealed: Initially determined innocent, but resulted in a mistrial due to certain evidence not being admitted and procedural errors.
Trial 2: Guilty
Appeal: Guilty
Final verdict: Guilty.
There was two trials due to the first ending in a mistrial, something that happens frequently in America as well. The common perception that Knox was ever found innocent is due to misunderstanding and poor explanation of civil law mechanics in the UK/US media.