  A group G acts infinitely transitively on a set Y if for every positive
integer m, its action is m-transitive on Y. Given a real affine algebraic
variety Y of dimension greater than or equal to two, we show that, under a mild
restriction, if the special automorphism group of Y (the group generated by
one-parameter unipotent subgroups) is infinitely transitive on each connected
component of the smooth locus of Y, then for any real affine suspension X over
Y, the special automorphism group of X is infinitely transitive on each
connected component of the smooth locus of X. This generalizes a recent result
by Arzhantsev, Kuyumzhiyan and Zaidenberg over the field of real numbers.
