New Spin(7) holonomy metrics admitting $G_2$ holonomy reductions and M-theory/IIA dualities

We construct several Spin(7) holonomy metrics which admit a $G_2$ holonomy reduction along one isometry. The resulting $G_2$ holonomy metrics admit a further reduction to 6-dimensional Kahler metrics, therefore realizing the pattern Spin(7) $\to G_2\to$ (Kahler) proposed by Kaste et al., and which describe an M-theory/IIA superstring duality. An infinite class of such metrics are found, which are locally $R^3$-fibrations over the Eguchi-Hanson gravitational instanton and which, to our knowledge, were not considered in the literature before. Some of the supersymmetric cycles inside these metrics are characterized. At the end the constructed $G_2$ holonomy examples are lifted to a non geometrical IIA supergravity solution.