  We provide a rigorous numerical computation method to validate periodic,
homoclinic and heteroclinic orbits as the continuation of singular limit orbits
for the fast-slow system $x' = f(x,y,\epsilon), y' = \epsilon g(x,y,\epsilon)$
with one-dimensional slow variable $y$. Our validation procedure is based on
topological tools called isolating blocks, cone condition and covering
relations. Such tools provide us with existence theorems of global orbits which
shadow singular orbits in terms of a new concept, the covering-exchange.
Additional techniques called slow shadowing and $m$-cones are also developed.
These techniques give us not only generalized topological verification
theorems, but also easy implementations for validating trajectories near slow
manifolds in a wide range, via rigorous numerics. Our procedure is available to
validate global orbits not only for sufficiently small $\epsilon > 0$ but all
$\epsilon$ in a given half-open interval $(0,\epsilon_0]$. Several sample
verification examples are shown as a demonstration of applicability.
