Use either tcpdump (a command-line utility) or wireshark (a GUI tool).

Wireshark is somewhat easier to use, it will capture all traffic from your network interface. You'd start a capture with wireshark, then go to your browser and do the transaction you want to do, then back in wireshark you just need to identify an http packet (they're clearly marked as such in the capture), right-click and select "follow tcp stream". This will show you the whole conversation including http headers, which should in turn include the redirects.

Tcpdump in essence does the same: it intercepts network traffic and lets you look at it, but since (AFAIK) it has no knowledge of specific protocols, it's up to you to make sense of the captured traffic.

One other option is for you to install the Live HTTP headers extension for Firefox. When you enable it, it will capture the request as sent by your browser, any responses sent by the server including redirects. It's potentially easier to use than Wireshark but it's limited to showing you headers from the browser.