So when travelling you are to start the phases over from the beginning, regardless of what phase you just completed when one of the Blip piles goes empty?  Or, do you continue with the next phase after you complete the 4 steps of travel?

 I am assuming you keep going with the next phase as a new Event card might not be flipped and you would be using an old Event card to spawn swarms?

You continue with whatever Phase would normally come after Travel, you don't "reset" the turn to the beginning. Granted, mostly you'll travel at the end of the Event Phase, so the next Phase will be Choose Actions. Sometimes (Teleportarium), you can Travel during Phase 2, meaning the next one would be GS Attack Phase.

Thanks.  I did travel from the Teleportarium location so maybe that is why I was confused.  Played again tonight and I think I got the hang of it.  Off to play another round right now…

I have travelling down now but I'm still confused about the Teleportarium location card.  I flipped an event card which ended up emptying one blip pile.  So I travelled after the Event Phase was over.  The location card that came up was Teleportarium which makes you roll a die for each terminator.  I did that then the final "upon entering" step for Teleportarium is discard both blip piles. 

So instant travel to the next location before I do the next phase right?  Or would I do the Chose Actions phase before travelling, Chose Actions being the next Phase after my last Phase which was Event?

It is not 'Upon Entering', it is 'Activate Control Panel'.  You only follow those instructions if you choose to activate the control panel in the Teleportarium.

Ahh, I guess it helps if I actually read the Teleportarium card completely.  Thank you.