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POUR boiling water over tomatoes in small bowl; let stand 10 min.
DRAIN tomatoes, reserving liquid. Place reserved liquid, Neufchatel and pesto in blender; blend until smooth. Add tomatoes; blend just until combined. (A few chunks can remain.) Spoon into bowl.
REFRIGERATE 1 hour.
TOP each cracker with 1 tsp. Neufchatel mixture and 1 artichoke piece just before serving.