  We present a comprehensive study of strain-induced topological magnon phase
transitions in insulating three-dimensional (3D) topological chiral
antiferromagnets on the kagome-lattice. We show that by applying (100) uniaxial
strain, 3D insulating antiferromagnetic Weyl magnons (WMs) manifest as an
intermediate phase between a strain-induced 3D magnon Chern insulator (MCI)
with integer Chern numbers and a 3D trivial magnon insulator with zero Chern
number. In addition, we show that strain suppresses the topological thermal
Hall conductivity of magnons in these systems. Due to the similarity between 3D
insulating and metallic kagome chiral antiferromagnets, we envision that the
current results could also manifest in the 3D antiferromagnetic topological
Weyl semimetals Mn$_3$Sn\slash Ge.
