Using a reliable pt and having decent skills with them is very useful when getting away from these monsters. Stamina is essential to getting away so when you can hear their elemental attacks just roll left or right taking advantage of their terrible turn radius and most of the time totally ignoring any of their damage. Last thing is fly through trees or places where the wyvern would get distracted/stuck, like in Val where there's packs of mammoth that they will aggro onto instead of you
Stealing an egg is easiest when two people go one carries the other on the mount. If things get bad the carried person throws the egg on the flying mount and lets go...the wyverns will still chase him and not the person on the mount now with the egg.
This applies to Ragnarok only:
On the far west side of the Wyvern Trench there are usually an egg or two in the first couple of holes in the wall.
The coordinates (47.0, 51.4) (42.7, 55.4) (44.4, 58.8) and (33.5, 66.8) contain Ice Wyvern eggs. I can confirm the first and last have eggs, while I have only heard that the other two contain them.
The best way to fight alpha wyverns is with a tamed fire wyvern. Because all alphas are fire type, they cannot hurt you with their breath attack (although you can't hurt them with it either) but melee does much more damage anyways