Attacking unconnected continents...

[CerberusIV]

One refinement that is worthwhile if you are worried about that first captured city culture flipping back is to pound it down to a small size, capture it, move a settler in on a transport, move the transport back out (very important ), disband the city and build a new city with your settler, all in one turn.

Hey presto, a city with no residual culture and no foreign citizens so much less chance of flipping (no chance at all unless it has a tile overlap with an enemy city).

You do need to reduce the target city to a small size first in order to be able to disband it immediately but I would do that anyway to reduce the defensive bonus to help my marines.

This isn't strictly necessary but I feel it does give me a more secure base on the other continent.

[minke19104]

Or...

with PTW, when you capture the city with marines just abandon it. This way you'll get free slave workers. Use one of your worker to make an airfield terrain improvement.
Your worker will dissapear and turn into an airfield but who cares.... After that immidiately in the same turn send your Mech Infantries and Tanks by airdrops.

This is much cheaper than a rushed airport, since the worker that turned into an airfield is not evenr yours. The main drawback is that there wont be any fortify in city defense bonus. However if you by chance get 2 workers from the abandoned city, make 1 into an airfield and another one into a radar tower. Make sure u defend it though..

[Centauri18]

I usually capture a large city, then build an airport. First you use your forces to occupy the cioty until the resistance has worn itself out and to defend against enemy attacks, then once the resistance is over, rush build an airport, build a few defensive units, then attack. You can build offensive units in your homeland, then airlift them over to the enemy continent. The only problem is you can't airlift workers to start building railroads and such once the enemy is taken care of. I guess you just start building said workers or raze a few enemy cities, and put the population to work.
Well, that works for me, anyway. I never use nukes.