We report results from an atomistic molecular dynamics simulation study of ring-linear poly(ethylene oxide) (PEO) melts followed by a topological reduction to ensembles of primitive paths and a detailed geometric analysis using vector calculus, which reveals considerable cyclic threading by the linear chains. The simulations have been conducted using ring-linear PEO blends of the same size, over a series of molecular lengths and compositions. For PEO melts characterized by molecular weight (MW) greater than 10044 g/mol, in particular, our computations reveal the occurrence of multiple threading events (penetrations). We further find that the time it takes a linear molecule that threads a cyclic one to fully pass through the latter can be more than 1 order of magnitude larger than the corresponding relaxation time of the ring in its own melt. Our analysis implies that dynamics in ring-linear polymer blends is highly heterogeneous, with many of the threadings being long-lived and with the linear chains (even when present in small amounts) dramatically obstructing the mobility of rings.