Exact Lagrangian cobordism and pseudo-isotopy

We show that under some topological assumptions, an exact Lagrangian cobordism $(W;L_0,L_1)$ of dimension $dim(W)>5$ is a Lagrangian pseudo-isotopy. This result is a weaker form of a conjecture proposed by Biran and Cornea, which states that any exact Lagrangian cobordism is Hamiltonian isotopic to a Lagrangian suspension.