There are gaps between invertebrate-vertebrate

Claim

No fossils have been found transitional between invertebrates and vertebrates.

Actually, there are a fair number of Chordate fossils which have a supporting rod of tissue which seems to be the predecessor to a spine, including Pikaia gracilens, Haikouichthys, and the conodonts.
Note the phylum Chordata. Many species exist which are invertebrate but still chordate. One of the requirements for classification as a chordate is a notochord. There are craniates that have a vertebral column but do not have mandibles. There is one species with all the other craniate features but none have a notochord with some neural arches (bony) on the notochord. There is also another 'fish' which has very similar features but lacks neural arches on the notochord. Finally consider acorn worms, such as Balanoglossus. It has a hollow dorsal nerve chord and pharyngeal gill slits, two characteristic chordate features, but lacks a notochord. We are hence able to see the evolution of non-chordates to chordates to vertebrates not through transitional fossils but through living, breathing creatures that are in existence today.
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Monastersky, R., 1999. (see above).
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