Maneka Gandhi is supposed to have said that scientifically relocation of cheetah’s was not possible.

 Dr R L Eaton, who had worked on charismatic species like Cheetah was of the view that these animals should not be transported.

I am also quoting the impact on tigers from a paper by Dembiec, D.P, Snider, R.J and Zanella, A.J. (2004) in the paper “The effects of transport stress on tiger Physiology and behaviour”, Zoo Biology.

"Tigers are often transported for education, conservation, and zoo enhancement purposes, however the effect of transfer on them has not yet been documented. Our objective was to evaluate how transport affects the behavior and physiology of tigers, taking into account previous experience with the transport procedure.

We simulated transport by relocating five tigers in a small individual transfer cage. Two tigers had prior experience with the procedure, and three tigers were naive to it. After 30 min, each tiger was released back into their original enclosure. Physiological measurements were recorded for four of the five tigers; these included respiration rate and immune-reactive fecal cortisol response using radioimmunoassay. We also recorded the behavior of all five tigers before, during, and after transport. Our behavioral analysis included activity level, pacing behavior, time spent investigating, respiration rate, and ear position. Average respiration rates of all tigers increased from 56.1 breaths/min to 94.6 breaths/min during transport and to 132.3 breaths/min 10 min following release into their enclosures. Average immune-reactive cortisol concentrations peaked 3-6 days after transport at 239% above baseline and returned to baseline levels 9-12 days afterward. During their peak time block, naive tigers exhibited a higher average increase in cortisol levels (482% above baseline) than the experienced tigers (158% above baseline). The naive tigers\' average immune-reactive cortisol concentration remained elevated for a longer period (9-12 days) than the experienced tigers\' (3-6 days). In both groups, behavioral responses ranged from active to inactive, however naive tigers performed these repertoires with greater intensity by pacing faster and performing fewer state changes. Results suggest that prior exposure to elements of the transport procedure may lead to some level of habituation, thus reducing the effects of transportation stress. 2004 Wiley-Liss, Inc".
It should be noted that the above experiment was done in a zoo. And it didn't entail transcontinent relocation.

Sabyasachi