First of all you need to consider, that both LP and Anti live from the spin that YOU put into the ball. Non of the rubber will allow the opponent player to generate spin. So play without spin from the start and don't mind how he/she holds the racket when doing a stroke, there is no spin in return. This is the hardest part for most "newbies" to ANTI of LP. You see a push stroke and assume you get under spin, but instead get a flat ball.
What I do usually...Flat serve with no spin into the anti and try to shot the next ball.
Be aware that the ball will have a lot less speed/length and will stop more suddenly. So stay closer to the table.
Be aware that the opponents serves will also have no spin, regardless of the racket motion.
If you want to play with spin, be aware that you get the opposite spin back. I sometimes do a serve with heavy under spin into the ANTI (sometime they drop them into the net), but if you get it back it very similar to a block top spin ball. So you have to close the racket and play it accordingly. The next ball which comes back (regardless of LP or ANTI) will have heavy under spin (based on how many top spin you generated).
So it requires some concentration, but basically the spin is predictable because it simply reversed from what you put in (easier said then done).
Try to avoid side spin a all means, because the results coming back will be reversed in spin as well, but will look very strange during the flight towards you.
Good luck....