Travelling via the US for an ex overstayed visa traveller?

Back in Dec 2003 when I was younger and stupider, I left the US to go back to the UK (I am a UK citz), after overstaying my visa by 3 years - I went to the US in 2000. I totally understand this was my choice, my fault, and I broke the rules, and I can accept why the US wouldnt want me to travel back in to their country, but I was wondering if I could still fly to other countries via the US, on the transit visa?