hope everyone is staying safe during this period of the year.
In contact geometry, one endows a manifold $M$ with a contact form, which is a one-form $\alpha$ such that $(d\alpha)^n\rvert_{\ker \alpha}$ is symplectic (up to conformal classes). Their "almost" counterpart are (once again up to conformal classes) pairs $(\alpha,\eta)$ such that $\eta$ is symplectic on $\ker \alpha$.
A result from Borman-Eliashberg & Murphy states that any almost contact structure $\eta$ on a manifold $M$ is homotopic to a contact structure $\xi$. My question is as follows: what is meant with homotopic?
As far as I understand, which is quite limited on this topic, they talk about homotopies "in the space of (almost) contact structures of the manifold". What topology do we endow such a space with? What kind of space is this?
Any help is greatly appreciated!