  The global dynamics of a nonautonomous Carath\'eodory scalar ordinary
differential equation $x'=f(t,x)$, given by a function $f$ which is concave in
$x$, is determined by the existence or absence of an attractor-repeller pair of
hyperbolic solutions. This property, here extended to a very general setting,
is the key point to classify the dynamics of an equation which is a transition
between two nonautonomous asypmtotic limiting equations, both with an
attractor-repeller pair. The main focus of the paper is to get rigorous
criteria guaranteeing tracking (i.e., connection between the attractors of the
past and the future) or tipping (absence of connection) for the particular case
of equations $x'=f(t,x-\Gamma(t))$, where $\Gamma$ is asymptotically constant.
Some computer simulations show the accuracy of the obtained estimates, which
provide a powerful way to determine the occurrence of critical transitions
without relying on a numerical approximation of the (always existing) locally
pullback attractor.
