Union of cones along a common base
= Union of cones along a common base
The union of $m$ cones on a nonempty space along one common base is homotopy equivalent to a wedge of $m-1$ suspensions of that space.
= Union of cones along a common base
The union of $m$ cones on a nonempty space along one common base is homotopy equivalent to a wedge of $m-1$ suspensions of that space.